BEGIN:VCALENDAR
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CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:Michael Shapiro
DTSTART:20230712T073000Z
DTEND:20230712T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/1
DESCRIPTION:Title: Symplectic groupoid and Teichmuller space of closed genus two
curves (continued)\nby Michael Shapiro as part of Moscow-Beijing topol
ogy seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatiana Kozlovskaya
DTSTART:20230719T073000Z
DTEND:20230719T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/2
DESCRIPTION:Title: Braid-like group. Simplicial structure on pure singular braid
groups.\nby Tatiana Kozlovskaya as part of Moscow-Beijing topology sem
inar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seokbeom Yoon
DTSTART:20230802T073000Z
DTEND:20230802T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/3
DESCRIPTION:Title: Super-Ptolemy coordinates and C^2-torsion polynomial\nby S
eokbeom Yoon as part of Moscow-Beijing topology seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eiji Ogasa
DTSTART:20230809T073000Z
DTEND:20230809T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/4
DESCRIPTION:Title: Framed links in thickened surfaces and quantum invariants of 3
-manifolds with boundary\nby Eiji Ogasa as part of Moscow-Beijing topo
logy seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Sergeev
DTSTART:20230726T073000Z
DTEND:20230726T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/5
DESCRIPTION:Title: Pentagon Identity and Multidimensional Integrability\nby S
ergei Sergeev as part of Moscow-Beijing topology seminar\n\nAbstract: TBA\
n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lin Jianfeng
DTSTART:20230816T073000Z
DTEND:20230816T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/6
DESCRIPTION:Title: Kontsevich's characteristic classes and formal smooth structur
es\nby Lin Jianfeng as part of Moscow-Beijing topology seminar\n\n\nAb
stract\nIn 2018\, Watanabe disproved the 4-dimensional Smale conjecture by
showing that the diffeomorphism group of a 4-dimensional disk relative to
its boundary is non-contractible. In Watanabe's proof he used a version o
f Kontsevich's characteristic classes to detect non-trivial smooth familie
s of disk bundles. In this talk we will show that Kontsevich's characteris
tic classes only depend the formal smooth structure\, i.e. a lift of the t
angent microbundle to a vector bundle. As an application\, we will prove t
hat for an arbitrary compact 4-manifold (with or without boundary)\, the f
orgetful map from diffeomorphism group to the homeomorphism group is not a
rational homotopy equivalence. And we will prove the same result for the
4-dimensional Euclidian space. This is joint work with Yi Xie (Peking U
niversity)\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lin Dexie (Chongqing university)
DTSTART:20230823T073000Z
DTEND:20230823T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/7
DESCRIPTION:Title: Kodaira type conjecture on almost complex 4 manifolds\nby
Lin Dexie (Chongqing university) as part of Moscow-Beijing topology semina
r\n\n\nAbstract\nIn this paper\, we define a refined Dolbeault cohomology
on almost complex manifolds. We show that the condition h 1\,0 = h˜0\,1 i
mplies a symplectic structure on a compact almost complex 4 manifold\, whe
re ˜h 0\,1 is the Hodge number of the refined Dolbeault cohomology and h
1\,0 is the Hodge number of the Dolbeault cohomology defined by Cirici and
Wilson [5]. Moreover\, we prove that the condition h 1\,0 = h˜0\,1 is eq
uivalent to ∂∂¯-lemma\, which is similar to the case of compact compl
ex surfaces. Meanwhile\, unlike compact complex surfaces\, we show that on
compact almost complex 4 manifolds the equality b1 = h 0\,1 +h 1\,0 does
not hold in general.\nhttps://arxiv.org/pdf/2307.14690.pdf\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tianyu Yuan
DTSTART:20230830T073000Z
DTEND:20230830T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/8
DESCRIPTION:Title: Folded Morse trees and spectral networks\nby Tianyu Yuan a
s part of Moscow-Beijing topology seminar\n\n\nAbstract\nWe present an app
roach to do Morse theory on symmetric products of surfaces\, and show its
relation to higher-dimensional Heegaard Floer homology (HDHF). As an appli
cation\, we recover the finite Hecke algebra by Morse theory. We also sket
ch the application to spectral networks. This is joint work with Ko Honda
and Yin Tian.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dilshan Wijesena
DTSTART:20230906T073000Z
DTEND:20230906T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/9
DESCRIPTION:Title: Classifying representations of the Thompson groups and the Cun
tz algebra\nby Dilshan Wijesena as part of Moscow-Beijing topology sem
inar\n\n\nAbstract\nRichard Thompson’s groups $F$\, $T$ and $V$ are one
of the most remarkable discrete infinite groups for their several unusual
properties. On the other hand\, the celebrated Cuntz algebra has many fasc
inating properties and it is known that $V$ embeds inside the Cuntz algebr
a. However\, classifying the representations of the Thompson groups and th
e Cuntz algebra have proven to be very difficult.\n\nLuckily\, thanks to t
he novel technology of Vaughan Jones\, a rich family of so-called Pythagor
ean representation of the Thompson groups and the Cuntz algebra can be con
structed by simply specifying a pair of finite-dimensional operators satis
fying a certain equality. These representations carry a powerful diagramma
tic calculus which we use to develop techniques to study their properties.
This permits to reduce very difficult questions concerning irreducibility
and equivalence of infinite-dimensional representations into problems in
finite-dimensional linear algebra. Moreover\, we introduce the Pythagorean
dimension which is a new invariant for all representations of the Cuntz a
lgebra. For each dimension $d$\, we show the irreducible classes form a mo
duli space of a real manifold of dimension $2d^2+1$. Finally\, we introduc
e the first known notion of a tensor product for representations of the Cu
ntz algebra.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Lando (HSE University\, Skolkovo Institute of Science and T
echnology)
DTSTART:20230927T073000Z
DTEND:20230927T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/10
DESCRIPTION:Title: Weight systems related to Lie algebras\nby Sergei Lando (
HSE University\, Skolkovo Institute of Science and Technology) as part of
Moscow-Beijing topology seminar\n\n\nAbstract\nPlease check the link https
://disk.yandex.ru/i/6D1IjHqHG6mYlA\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fedor Duzhin
DTSTART:20230913T073000Z
DTEND:20230913T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/11
DESCRIPTION:Title: On two practical problems of social choice theory\nby Fed
or Duzhin as part of Moscow-Beijing topology seminar\n\n\nAbstract\nWe wil
l introduce two practical problems in the social choice theory. \nThe firs
t scenario is envy-free division. Here\, n friends are renting an n-bedroo
m apartment together. They need to split the rent and distribute the bedro
oms among themselves so that everyone is happy with their bedroom\, i.e.\,
no one would prefer someone else's room to their own (given the rent). We
will derive the existence of an envy-free division from Sperner's Lemma (
combinatorial analog of Brouwer's Fixed Point Theorem).\nThe second scenar
io is peer evaluation. Here\, n students work on a common task\, and the j
ob of the course instructor is to grade individual contributions to group
work. We assume that there exists an objective truth - a vector of individ
ual contributions that is known to students but not to the instructor. Stu
dents are required to do peer evaluation\, i.e.\, all team members report
their version of the truth. We will show then how the instructor can desig
n a method of grading that encourages students to report the truth (the co
llective truth-telling is a strict Nash equilibrium).\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fengling Li
DTSTART:20230920T073000Z
DTEND:20230920T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/12
DESCRIPTION:Title: The $F$-polynomial invariant for knotoids\nby Fengling Li
as part of Moscow-Beijing topology seminar\n\n\nAbstract\nAs a generaliza
tion of the classical knots\, knotoids deal with the open ended knot diagr
am in a surface. \n\nIn recent years\, many polynomial invariants for knot
oids appeared\, such as the bracket polynomial\, the index polynomial and
the $n$th polynomial\, etc. \n\nIn this talk\, we introduce a new polynomi
al invariant $F$-polynomial for knotoids and discuss some properties of it
. This is joint work with Yi Feng.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akio Kawauchi (Osaka Central Advanced Mathematical Institute\, Osa
ka Metropolitan University)
DTSTART:20231004T073000Z
DTEND:20231004T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/13
DESCRIPTION:Title: Ribbon disk-link realization of contractible finite 2-complex
and Kervaire conjecture on group weight\nby Akio Kawauchi (Osaka Cent
ral Advanced Mathematical Institute\, Osaka Metropolitan University) as pa
rt of Moscow-Beijing topology seminar\n\n\nAbstract\nKervaire conjecture t
hat the free product of every non-trivial group\nand the infinite cyclic g
roup is not normally generated by one element\nis confirmed. The idea is t
o solve Conjecture Z of a knot exterior proposed \nby F. Gonzalez-Acuna a
nd A. Ramirez as an equivalent conjecture. For this solution\,\na ribbon d
isk-link realization of a contractible finite 2-complex and the asphericit
y of\na ribbon disk-link are used.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dilshan Wijesena
DTSTART:20231025T073000Z
DTEND:20231025T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/14
DESCRIPTION:Title: Classifying representations of the Thompson groups and the Cu
ntz algebra\nby Dilshan Wijesena as part of Moscow-Beijing topology se
minar\n\n\nAbstract\nRichard Thompson’s groups $F$\, $T$ and $V$ are one
of the most remarkable discrete infinite groups for their several unusual
properties. On the other hand\, the celebrated Cuntz algebra has many fas
cinating properties and it is known that $V$ embeds inside the Cuntz algeb
ra. However\, classifying the representations of the Thompson groups and t
he Cuntz algebra have proven to be very difficult.\n\nLuckily\, thanks to
the novel technology of Vaughan Jones\, a rich family of so-called Pythago
rean representation of the Thompson groups and the Cuntz algebra can be co
nstructed by simply specifying a pair of finite-dimensional operators sati
sfying a certain equality. These representations carry a powerful diagramm
atic calculus which we use to develop techniques to study their properties
. This permits to reduce very difficult questions concerning irreducibilit
y and equivalence of infinite-dimensional representations into problems in
finite-dimensional linear algebra. Moreover\, we introduce the Pythagorea
n dimension which is a new invariant for all representations of the Cuntz
algebra. For each dimension $d$\, we show the irreducible classes form a m
oduli space of a real manifold of dimension $2d^2+1$. Finally\, we introdu
ce the first known notion of a tensor product for representations of the C
untz algebra.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassily O. Manturov
DTSTART:20231011T073000Z
DTEND:20231011T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/15
DESCRIPTION:Title: Flat-virtual objects or how to map classical theory to virtua
l theory\nby Vassily O. Manturov as part of Moscow-Beijing topology se
minar\n\n\nAbstract\nVirtual knot theory is a proper generalisation of cla
ssical knot theory. It is known that virtual knots\nand links admit many p
owerful invariants and techniques that never appeared in classical knot th
eory.\n In the talk we construct a map from braids\, knots and links in th
e full torus to (closed relatives of) virtual\nbraids\, knots\, and links.
\n The talk is based on joint papers of the speaker with I.M.Nikonov:\narX
iv:2210.06862\narXiv:2210.09689\n Many unsolved problems will be stated.
Many research projects will be formulated.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rhea Bakshi Palak
DTSTART:20231115T073000Z
DTEND:20231115T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/16
DESCRIPTION:Title: On the structure of the Kauffman bracket skein module\nby
Rhea Bakshi Palak as part of Moscow-Beijing topology seminar\n\n\nAbstrac
t\nSkein modules were introduced by Józef H. Przytycki as generalisations
of the Jones and HOMFLYPT polynomial link invariants in the 3-sphere to a
rbitrary 3-manifolds. The Kauffman bracket skein module (KBSM) is the most
extensively studied of all. However\, computing the KBSM of a 3-manifold
is known to be notoriously hard\, especially over the ring of Laurent poly
nomials. With the goal of finding a definite structure of the KBSM over th
is ring\, several conjectures and theorems were stated over the years for
KBSMs. We show that some of these conjectures\, and even theorems\, are no
t true. In this talk I will briefly discuss a counterexample to Marche’s
generalisation of Witten’s conjecture. I will show that a theorem state
d by Przytycki in 1999 about the KBSM of the connected sum of two handlebo
dies does not hold. I will also give the exact structure of the KBSM of of
the connected sum of two solid tori and show that it is isomorphic to the
KBSM of a genus two handlebody modulo some specific handle sliding relati
ons. Moreover\, these handle sliding relations can be written in terms of
Chebyshev polynomials. I will also discuss the structure of the skein modu
le of $S^1 \\times S^2 \\ \\# \\ H_1$ and $S^1 \\times S^2 \\ \\# \\ S^1 \
\times S^2$. Parts of this talk are based on joint work with Thang Le\, J
ózef Przytycki\, Seongjeong Kim\, and Xiao Wang.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hayk Sedrakyan
DTSTART:20231122T053000Z
DTEND:20231122T070000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/18
DESCRIPTION:Title: Distance formulas for any four points on a plane. Possible ap
plications to pentagon case\nby Hayk Sedrakyan as part of Moscow-Beiji
ng topology seminar\n\n\nAbstract\nGiven a connected graph with four verti
ces and six edges (a quadrilateral and its diagonals). We obtained a novel
formula to find the length of any of its edges using the other five edge
lengths. We are interested in possible applications of this formula to pen
tagon case.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haimiao Chen
DTSTART:20231206T073000Z
DTEND:20231206T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/19
DESCRIPTION:Title: Torsion in the skein module of the complement of a 4-strand M
ontesinos knot\nby Haimiao Chen as part of Moscow-Beijing topology sem
inar\n\n\nAbstract\nFor a 3-manifold M\, let S(M) denote its Kauffman brac
ket skein module. Problem 1.92 (G) (i) in the Kirby's list asks whether S(
M) is free when M is irreducible and has no incompressible non-parallel to
the boundary torus. We answer this negatively by showing that S(M) contai
ns torsion when M is the complement of a 4-strand Montesinos knot in the 3
-sphere.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Yakovlevich Kanel-Belov
DTSTART:20231213T073000Z
DTEND:20231213T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/20
DESCRIPTION:Title: Quantization\, polynomial automorphisms and the Jacobian prob
lem.\nby Alexey Yakovlevich Kanel-Belov as part of Moscow-Beijing topo
logy seminar\n\n\nAbstract\nLet F: Cn→ Cn be a polynomial mapping of a c
omplex space into itself. When is it reversible? A necessary condition is
local invertibility at each point. The famous Jacobian problem states that
this condition is sufficient. For more than 20 years\, until 1968\, the J
acobian problem was considered solved for n = 2\, since then new “eviden
ce” has appeared every few months.\n\nThe Jacobian problem is closely re
lated to the Dixmier conjecture\, the formulation of which for n=1 looks i
nnocent: let P\, Q be polynomials in x and (d/dx)\, and PQ– QP=1. Is it
true that (d/dx) can be expressed in terms of P and Q. This statement has
not yet been proven. Recently it was possible to prove the equivalence of
this statement to the Jacobian problem for n=2. The stable equivalence of
the Jacobian and Dixmier conjectures is proven in the work http://arxiv.or
g/abs/math/0512171. The proof uses an analogy between classical and quantu
m objects. It is intended to give an elementary explanation of this analog
y and also discuss Kontsevich’s hypotheses.\n\nAnother\, close\, stateme
nt is called the Abiencar–Moch theorem and looks like an Olympiad proble
m (which it is). Let P\, Q\, R be polynomials\, and R(P(x)\,Q(x))=x. Prove
that either the degree of P divides the degree of Q\, or vice versa.\n\nT
he first part of the report is an introduction to the problem and is suppo
sed to be quite elementary\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassily Olegovich Manturov
DTSTART:20231220T073000Z
DTEND:20231220T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/21
DESCRIPTION:Title: A map from classical theory to virtual knot theory. An introd
uction to flat-virtual knots\nby Vassily Olegovich Manturov as part of
Moscow-Beijing topology seminar\n\n\nAbstract\nProfessor Manturov will ta
lk in more detail about two constructions suggested in the papers https://
arxiv.org/abs/2210.06862\, https://arxiv.org/abs/2210.09689 where classica
l objects (classical braid\, knots in the full torus and knots in the thi
ckened torus) are mapped analogues of virtual knots: the so-called flat-v
irtual knots. Professor Manturov will discuss various invariants of the la
tter leading to lots of invariants of classical objects\, generalising the
Burau representation\, Kauffman bracket\, and many other objects. Many un
solved problems will be formulated during the talk.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chen Xiaoyang
DTSTART:20240103T073000Z
DTEND:20240103T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/22
DESCRIPTION:Title: Rational ellipticity of Riemannian manifolds\nby Chen Xia
oyang as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIt was con
jectured by Bott-Grove-Halperin that a compact simply connected Riemannian
manifold with nonnegative sectional curvature is rationally elliptic\, i.
e.\, it has finite dimensional rational homotopy groups. We will discuss s
ome recent progress on this conjecture.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ren Shiquan
DTSTART:20231227T073000Z
DTEND:20231227T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/23
DESCRIPTION:Title: Regular maps on Cartesian products and disjoint unions of man
ifolds\nby Ren Shiquan as part of Moscow-Beijing topology seminar\n\n\
nAbstract\nA map from a manifold to a Euclidean space is said to be k-regu
lar if the images of any distinct k points are linearly independent. For k
-regular maps on manifolds\, lower bounds on the dimension of the ambient
Euclidean space have been extensively studied. In this talk\, we study the
lower bounds on the dimension of the ambient Euclidean space for 2-regula
r maps on Cartesian products of manifolds. As corollaries\, we obtain the
exact lower bounds on the dimension of the ambient Euclidean space for 2-r
egular maps and 3-regular maps on spheres as well as on some real projecti
ve spaces. Moreover\, generalizing the notion of k-regular maps\, we study
the lower bounds on the dimension of the ambient Euclidean space for maps
with certain non-degeneracy conditions from disjoint unions of manifolds
into Euclidean spaces.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Dobritsyn
DTSTART:20240110T073000Z
DTEND:20240110T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/24
DESCRIPTION:by Mikhail Dobritsyn as part of Moscow-Beijing topology semina
r\n\n\nAbstract\nThe van der Waerden’s theorem is an important result in
combinatorics of arithmetic progressions. It turns out\, this theorem is
easily solvable in agame from and winning strategy requires much fewer mov
es to win.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiyun Cheng
DTSTART:20240117T073000Z
DTEND:20240117T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/25
DESCRIPTION:Title: The calculation of the rank of the incidence matrix of a hype
rgraph\nby Zhiyun Cheng as part of Moscow-Beijing topology seminar\n\n
\nAbstract\nIn this talk\, I will explain how to calculate the rank of the
incidence matrix of a hypergraph. Several concrete examples will be discu
ssed.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhang Zhi-Hao
DTSTART:20240124T073000Z
DTEND:20240124T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/26
DESCRIPTION:Title: Enriched categories and their centers\nby Zhang Zhi-Hao a
s part of Moscow-Beijing topology seminar\n\n\nAbstract\nThe notion of an
enriched (fusion) category naturally appears in the study of the mathemati
cal theory of topological orders. In this talk\, I will introduce a symmet
ric monoidal 2-category of enriched categories with arbitrary background c
ategories. Then the notion of an enriched (braided or symmetric) monoidal
category can be defined as an E_n-algebra in this 2-category. Finally I wi
ll introduce the notion of a center and compute the center of an enriched
(monoidal or braided monoidal) category. This talk is based on a joint wor
k arXiv:2104.03121 with Liang Kong\, Wei Yuan and Hao Zheng.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Dmitrievich Mednykh
DTSTART:20240131T073000Z
DTEND:20240131T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/27
DESCRIPTION:Title: Spectral Invariants of Graphs and Their Applications to Combi
natorics.\nby Alexander Dmitrievich Mednykh as part of Moscow-Beijing
topology seminar\n\n\nAbstract\nWe present recent results obtained by the
authors. They are related to spectral invariants of graphs admitting an ar
bitrary large cyclic group action. To illustrate them we use the family of
circulant graphs G_n = C_n(s_1\, s_2\, . . . \, s_k). The Chebyshev polyn
omials provide a significant analytical tools for studying the properties
of such graphs and their characteristic polynomials. In particular\, this
gives a way to find analytical expressions for the number of spanning tree
s τ(n)\, the number of rooted spanning forests f_{G}(n) and the Kirchhoff
index Kf(G_n) of a graph. We are interested in the behaviour of these inv
ariants for sufficiently large n. We provide asymptotic formulas of the ab
ove mentioned invariants. These results were motivated by problems arising
in theoretical physics\, biology and chemistry.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kodai Wada (Kobe University)
DTSTART:20240207T073000Z
DTEND:20240207T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/28
DESCRIPTION:Title: Virtualized Delta moves for virtual knots and links\nby K
odai Wada (Kobe University) as part of Moscow-Beijing topology seminar\n\n
\nAbstract\nWe introduce a local deformation called a virtualized Delta mo
ve for unoriented virtual knots and links. We prove that it is an unknotti
ng operation for unoriented virtual knots\, and give a necessary and suffi
cient condition for two unoriented virtual links of two or more components
to be related by a finite sequence of virtualized Delta moves. We also ta
lk about virtualized Delta\, sharp\, and pass moves for oriented virtual k
nots and links. This is a joint work with Takuji Nakamura\, Yasutaka Nakan
ishi\, and Shin Satoh.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Lando
DTSTART:20240221T073000Z
DTEND:20240221T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/29
DESCRIPTION:Title: Inducing graph invariants from the universal $\\mathcal{gl}$-
weight system\nby Sergei Lando as part of Moscow-Beijing topology semi
nar\n\n\nAbstract\nWeight systems\, which are functions on chord diagrams
satisfying certain 4-term relations\, appear naturally in Vassiliev's theo
ry of nite type knot invariants.\nIn particular\, a weight system can b
e constructed from any nite dimensional\nLie algebra endowed with a non
degenerate invariant bilinear form. Recently\,\nM. Kazarian suggested to e
xtend the $gl(N)$-weight system from chord diagrams\n(treated as involutio
ns without xed point) to arbitrary permutations\, which\nled to a recur
rence formula allowing for an e ective computation of its values\,\nelab
orated by Zhuoke Yang. In turn\, the recurrence helped to unify the $\\mat
hcal{gl}(N)$\nweight systems\, for $N = 1\, 2\, 3\,\\dots$\, into a univer
sal gl-weight system. The\nlatter takes values in the ring of polynomials
$\\mathbb{C}[N][C_1\,C_2\,\\dots]$ in in nitely many variables $C_1\,C_2
\,\\dots$ (Casimir elements)\, whose coe cients are polynomials in $N$.\
nThe universal $\\mathcal{gl}$-weight system carries a lot of information
about chord\ndiagrams and intersection graphs. The talk will address the q
uestion which graph\ninvariants can be extracted from it. We will discuss
the interlace polynomial\,\nthe enhanced skew-characteristic polynomial\,
and the chromatic polynomial. In\nparticular\, we show that the interlace
polynomial of the intersection graphs can\nbe obtained by a speci c subs
titution for the variables $n\,C_1\,C_2\,\\dots$. This allows\none to exte
nd it from chord diagrams to arbitrary permutations.\nQuestions concerning
other graph and delta-matroid invariants and their\npresumable extensions
will be formulated.\nThe talk is based on a work of the speaker and a PhD
student Nadezhda\nKodaneva.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20240228T073000Z
DTEND:20240228T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/30
DESCRIPTION:Title: Knot in $S_{g}\\times S^{1}$ of degree one and long knot inva
riants\nby Seongjeong Kim as part of Moscow-Beijing topology seminar\n
\n\nAbstract\nIn this talk we construct invariants for knots in $S_{g}\\ti
mes S^{1}$ of degree one by using long knot invariants.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiang Yi
DTSTART:20240320T073000Z
DTEND:20240320T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/32
DESCRIPTION:Title: Free circle actions on highly connected (2n+1)-manifolds\
nby Jiang Yi as part of Moscow-Beijing topology seminar\n\n\nAbstract\nA n
atural problem in topology is to determine which manifolds admit certain g
roup actions. The problem we concern in this talk is to determine which hi
ghly connected (2n+1)-manifolds admit free circle actions. I will introduc
e some previous work and our progress on this problem. This is a joint wor
k with Yang Su.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kirova Valeriia
DTSTART:20240306T073000Z
DTEND:20240306T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/33
DESCRIPTION:Title: On the combinatorial complexity functions of Sturmian words\nby Kirova Valeriia as part of Moscow-Beijing topology seminar\n\n\nAbs
tract\nConsider combinatorial complexity functions of infinite words\, esp
ecially factor complexity and its modifications. First of all\, we present
an overview of the available results for Sturmian words. Special attentio
n is paid to the arithmetical complexity of infinite words\, the study of
which was initiated by Van der Waarden Theorem on one-color arithmetic pro
gressions. Arithmetical complexity is presented in a sense a modification
of factor complexity. An overview of current results and exact values of
arithmetic complexity for Sturmian words is presented. We present polynomi
al Van der Waerden Theorem\, which gives rise to the study of a more gene
ralized modification of the factor complexity function - the polynomial co
mplexity of infinite words.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco De Renzi
DTSTART:20240403T073000Z
DTEND:20240403T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/34
DESCRIPTION:Title: Homological and quantum representations of mapping class grou
ps\nby Marco De Renzi as part of Moscow-Beijing topology seminar\n\n\n
Abstract\nFor a connected surface Σ with connected boundary\, there exist
two very different constructions of the same family of representations of
the mapping class group Mod(Σ): one comes from the non-semisimple TQFT a
ssociated with the quantum group of sl(2)\, while the other arises from tw
isted homology groups of configuration spaces of Σ. I will explain the
equivalence between the two actions\, and how this is expected to generali
ze in the presence of cohomology classes. This is based on joint works wit
h Jules Martel and Bangxin Wang.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Baptiste Meilhan
DTSTART:20240313T073000Z
DTEND:20240313T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/35
DESCRIPTION:Title: Cut-diagrams and surfaces in 4-space\nby Jean-Baptiste Me
ilhan as part of Moscow-Beijing topology seminar\n\n\nAbstract\nThe purpos
e of this talk is to define a family of (concordance and link-homotopy) in
variants of knotted surfaces in 4-space. The construction is modeled on Mi
lnor link invariants\, which are numerical concordance invariants of links
in 3-space\, extracted from the nilpotent quotients of the link group. Ou
r construction makes use of "cut-diagrams" of knotted surfaces in 4-space\
, which encode these objects in a simple combinatorial way. Roughly speaki
ng\, for a knotted surface obtained as embedding of the abstract surface S
\, a cut-diagram is a kind of 1-dimensional diagram on S with some labelin
g. We will provide several examples and applications. No expertise in 4-di
mensional topology is required for this talk. This is a joint work with Be
njamin Audoux and Akira Yasuhara.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ramanujan Santharoubane
DTSTART:20240410T073000Z
DTEND:20240410T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/36
DESCRIPTION:Title: An embedding of the Kauffman bracket skein algebra of a surfa
ce into a localized quantum torus\nby Ramanujan Santharoubane as part
of Moscow-Beijing topology seminar\n\n\nAbstract\nI will explain how to bu
ild a new embedding of the Kauffman bracket skein algebra of a surface int
o a localized quantum torus via Dehn-Thurston coordinates. The quantum tor
us is said to be localized because certain extra elements need to be inver
ted. An important property is that the localized quantum torus is somehow
a finite extension of the skein algebra. As an application I will show how
to recover a proof of the unicity conjecture already proved by Frohman\,
Kania-Bartoszynska and Lê. An explicit description of most irreducible re
presentations of the skein algebra at root of unity will be possible.\nThi
s is joint work with Renaud Detcherry.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benoît Guerville-Ballé
DTSTART:20240327T073000Z
DTEND:20240327T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/37
DESCRIPTION:Title: Connectedness and combinatorial interplay in the moduli space
of line arrangements.\nby Benoît Guerville-Ballé as part of Moscow-
Beijing topology seminar\n\n\nAbstract\nThe moduli space of a line arrange
ment (also known as the realization space) captures important topological
and geometric information about the arrangement. Due to Mnëv’s Universa
lity Theorem\, such moduli spaces can behave as wild as one can imagine. F
urthermore\, the Pappus configuration shows that unexpected collinearity c
an appear among the singular points of an arrangements. In this talk\, and
despite these results\, we focus on extracting topological information on
the moduli space of line arrangements using only combinatorial techniques
. In the first part\, we investigate the combinatorial class of inductivel
y connected line arrangements defined by Nazir and Yoshinaga. These arrang
ements are characterized by a recursive structure that ensures their modul
i space to be an open Zariski subset of an irreducible algebraic variety\,
and so to be path-connected. The second part will be devoted to a continu
ation of their work. For any fixed line arrangement\, we inductively compu
te a combinatorial upper-bound of the number of connected components of th
e moduli space. Our bound is based on a fine study of the equations govern
ing the incidence relations\, and more particularly of their degrees. It i
s shown to be sharp even for moduli space with an arbitrary large number o
f connected components. This is a joint work with Juan Viu-Sos.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Audoux
DTSTART:20240515T073000Z
DTEND:20240515T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/38
DESCRIPTION:Title: Welded graphs\, Wirtinger presentations and knotted punctured
spheres\nby Benjamin Audoux as part of Moscow-Beijing topology semina
r\n\n\nAbstract\nIn this talk\, I will introduce welded graphs\, that can
be seen as combinatorial objects lying between 3-dimensional knots and 4-d
imensional knotted surfaces. For these objects\, I will define a notion of
peripheral system from which I will extract Milnor invariants. This will
lead to a complete classification of knotted punctured spheres (with trivi
ally embedded boundary) up to link-homotopy.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Hass
DTSTART:20240417T073000Z
DTEND:20240417T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/39
DESCRIPTION:Title: Knotted surfaces and their profile curves\nby Joel Hass a
s part of Moscow-Beijing topology seminar\n\n\nAbstract\nThe profile curve
of a surface in R3 is formed from the points whose tangent plane is verti
cal. This is the "outline" of a surface. When a surface is transparent\,
this curve is what is most visible to the eye. Profile curves play a rol
e in surface reconstruction\, the problem of reconstructing a surface from
photographs. In this talk I will investigate the relationship between the
knot type of a profile curve and that of the surface it lies on. For exa
mple\, I will answer the following question: Is there an unknotted torus
whose profile curves contain a component that is the standard trefoil knot
?\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruben Louis
DTSTART:20240424T073000Z
DTEND:20240424T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/40
DESCRIPTION:Title: On Nash resolution of (singular) Lie algebroids\nby Ruben
Louis as part of Moscow-Beijing topology seminar\n\n\nAbstract\nWe show t
hat any Lie algebroid A admits a Nash-type blow-up Nash(A) that sits in a
nice short exact sequence of Lie algebroids 0–>K–>p*A–>D–>0 with K
a Lie algebra bundle and D a Lie algebroid whose anchor map is injective
on an open dense subset. The base variety is a blowup determined by the si
ngular foliation of A. We provide concrete examples. Moreover\, we extend
the construction following Mohsen’s to singular subalgebroids in the sen
se of Androulidakis-Zambon.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qingying Deng
DTSTART:20240522T073000Z
DTEND:20240522T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/41
DESCRIPTION:Title: Partial-dual polynomial as a framed weight system\nby Qin
gying Deng as part of Moscow-Beijing topology seminar\n\n\nAbstract\nRecen
tly\, Chmutov proved that the partial-dual polynomial considered as a func
tion on chord diagrams satisfies the four-term relation. In this talk\, I
will introduce two generalization results about it (Communications in Math
ematics 31 (2023)\, no. 3\, 151–160\, and arXiv:2404.10216).\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Margarita Shevtsova\, Ivan Vorobiev
DTSTART:20240501T073000Z
DTEND:20240501T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/42
DESCRIPTION:Title: Symbolic dynamics\, First and Second digits of sequences\
nby Margarita Shevtsova\, Ivan Vorobiev as part of Moscow-Beijing topology
seminar\n\n\nAbstract\nThe talk will be devoted to an introduction to the
word theory and the description of several problems that it is concerned
with. We will call a ”word” an infinite sequence of symbols that is ge
nerated from a dynamical system.$M$ --- a compact metric space$U$ --- open
subspace of M$f : M \\rightarrow M$ is a homeomorphism of the compact int
o itself$x_0 \\in M$ — an initial point. It determine{s a sequence of sy
mbols\n\n$$\n\nw_n = \\begin{cases} a\, f^{(n)}(x_0)\\in U \\\\ b\, f^{(n)
}(x_0)\\not \\in U \\end{cases}\n\n$$\n\nWe will be investigating the diff
erent combinations of m consecutive symbols (”subwords”) that can be f
ound in such words depending on which dynamic system was used to generate
them. We will be looking at the famous Sturmian sequences\, some of their
generalizations and their Rauzy graphs in more detail. Several dynamic sys
tems and their implications will be discussed in more detail. Namely\, cir
cle rotation\, interval exchange transformation\, billiards\, the first di
git of $2^n$\, $n!$\, $2^{n^2}$ \, the second digit of $2^n$.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eiji Ogasa
DTSTART:20240731T073000Z
DTEND:20240731T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/43
DESCRIPTION:Title: Seifert surfaces for virtual knots\nby Eiji Ogasa as part
of Moscow-Beijing topology seminar\n\n\nAbstract\nWe introduce Seifert su
rfaces for virtual knots.\nVirtual knots are represented by knots in thick
ened oriented surfaces\,\nwhich may be a non-zero cycle. Although it may b
e a non-zero cycle\,\nwe can define Seifert surfaces for virtual knots.\n
We also define Seifert matrices associated with our new Seifert surfaces
.\nFurthermore\, by using our new Seifert matrices\,\nwe introduce the Ale
xander polynomials and the signature.\n Our Alexander polynomial of vir
tual knots can obstruct from being classical knots.It is mirror sensitive
as isotopy invariants.\n Our signature is mirror sensitive as diffeomorph
ic invariants.\nThis talk is based on the paper\,\n New invariants for vi
rtual knots via spanning surfaces\nJournal of knot theory and its ramifica
tions 2024 arXiv:2207.08129 [math.GT]\nwritten by András Juhász\, Louis
H. Kauffman\, and the speaker.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shen Dawei
DTSTART:20240508T073000Z
DTEND:20240508T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/44
DESCRIPTION:Title: The magnitude for algebras is a generalization of the Euler c
haracteristic\nby Shen Dawei as part of Moscow-Beijing topology semina
r\n\n\nAbstract\nWe investigate the magnitude for Nakayama algebras. Using
Ringel’s resolution quiver\, the existence and the value of rational ma
gnitude is given. As a result\, we show directly that two finite global di
mension criteria for Nakayama algebras are equivalent. This is a joint wor
k with Yaru Wu.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hayk Sedrakyan
DTSTART:20240529T073000Z
DTEND:20240529T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/45
DESCRIPTION:Title: Novel Sedrakyan-Mozayeni theorem\, and its applications in sc
ientific research in topology and geometry\nby Hayk Sedrakyan as part
of Moscow-Beijing topology seminar\n\n\nAbstract\nIn this presentation\, w
e consider several applications of the Sedrakyan-Mozayeni theorem. In part
icular\, we investigate how it can be applied in novel mathematical scient
ific research in topology and geometry to generalize the pentagon case of
the photography principle\, data transmission and invariants of manifolds.
We will also go in depth on the derivation of Sedrakyan-Mozayeni theorem\
, and explain current issues with the pentagon case of the photography pri
nciple. Besides having theoretical applications\, the formula can be used
in applied mathematics and lead to new real-world results. We will impleme
nt the formula into a code and generate several computer simulations appli
ed in novel mathematical scientific research in topology and geometry.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darya Popova
DTSTART:20240612T073000Z
DTEND:20240612T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/46
DESCRIPTION:Title: Flat virtual links and knot invariants\nby Darya Popova a
s part of Moscow-Beijing topology seminar\n\n\nAbstract\nIn the talk I wil
l review a way of constructing invariants of knots in S^3\, thickened toru
s and thickened cylinder that was introduced by V. O. Manturov and I. M. N
ikonov. The idea is to map the knots to flat virtual diagrams and use inva
riants of flat virtual diagrams. Besides I will talk about my findings on
the diagrams which we get by this approach and how they lead to a hypothes
is that the potential of this approach for getting very strong invariants
of knots is small.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Qiu (YMSC)
DTSTART:20240626T073000Z
DTEND:20240626T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/47
DESCRIPTION:Title: Moduli spaces of quadratic differentials: Abel-Jacobi maps an
d deformation\nby Yu Qiu (YMSC) as part of Moscow-Beijing topology sem
inar\n\n\nAbstract\nWe give correspondences between: 1. deformation of 3-C
alabi-Yau categories\; 2. partial compactification with orbifolding of mod
uli spaces and 3. taking sub-quotient of mapping class groups.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fedor Nilov
DTSTART:20240605T073000Z
DTEND:20240605T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/48
DESCRIPTION:Title: Webs from circles and lines\nby Fedor Nilov as part of Mo
scow-Beijing topology seminar\n\n\nAbstract\nWe give an overview of known
results related to webs from circles and lines in Blaschke-Bol problem and
discuss an idea to construct some new examples.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shuang Wu
DTSTART:20240814T073000Z
DTEND:20240814T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/50
DESCRIPTION:Title: Applications of GLMY theory in metabolomic networks of comple
x diseases\nby Shuang Wu as part of Moscow-Beijing topology seminar\n\
n\nAbstract\nHuman diseases involve metabolic alterations. Metabolomic pro
files have served as a biomarker for the early identification of high-risk
individuals and disease prevention. However\, current approaches can only
characterize individual key metabolites\, without taking into account the
ir interactions.This work have leveraged a statistical physics model to co
mbine all metabolites into bDSW networks and implement GLMY homology theor
y to analyze and interpret the topological change of health state from sym
biosis to dysbiosis.The application of this model to real data allows us t
o identify several hub metabolites and their interaction webs\, which play
a part in the formation of inflammatory bowel diseases.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Fu
DTSTART:20240619T073000Z
DTEND:20240619T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/51
DESCRIPTION:Title: Cohomology of partial quotients\nby Xin Fu as part of Mos
cow-Beijing topology seminar\n\n\nAbstract\nBuchstaber and Panov introduce
d the notion of the moment-angle complex Z. This space is defined as a uni
on of specific product spaces of discs and circles\, equipped with a natur
al action of a torus T. Topologically\, a moment-angle complex provides a
way to understand a simplicial toric variety through its quotient Z/H\, wh
ere H is a closed subgroup of T. The computation of the cohomology groups
and cup products for these quotient spaces involves techniques from combin
atorics\, algebra\, and homotopy theory. These techniques have application
s in various fields. This talk summarizes known results for computing such
cohomology and presents our new progress. Our new approach uses digraphs
to describe the weights that encode how the torus is twisted in the quotie
nt space.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Shapiro
DTSTART:20240703T073000Z
DTEND:20240703T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/52
DESCRIPTION:Title: Mystery of point charges after Gauss-Maxwell-Morse\nby Bo
ris Shapiro as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIn h
is 2 volume chef-d'oeuvre “Treatise of electricity and Magnetism” J.C.
Maxwell (among thousands of much more important claims) formulated the fol
lowing statement.\n\nGiven any configurations of N fixed point charges in
R^3\, the electrostatic field created by them has at most (N-1)^2 points o
f equilibrium.\n\nMaxwell’s arguments are incomplete and this problem wa
s considered much later by M.Morse and revitalised about two decades ago.
However Maxwell’s original claim is still open already in case of N=3 ch
arges. In my talk I will survey what is known in this direction and\, in p
articular\, formulate a calculus 1 problem which currently still remains u
nsolved.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yurii Belov
DTSTART:20240710T073000Z
DTEND:20240710T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/53
DESCRIPTION:Title: Spectral synthesis for systems of exponentials and reproducin
g kernels\nby Yurii Belov as part of Moscow-Beijing topology seminar\n
\n\nAbstract\nLet $x_n$ be a complete and minimal system of vectors in a H
ilbert space $H$. We say\nthat this system is hereditarily complete or adm
its spectral synthesis if any vector in $H$\ncan be approximated in the no
rm by linear combinations of partial sums of the Fourier\nseries with resp
ect to $x_n$. It was a long-standing problem whether any complete and\nmin
imal system of exponentials in $L^2(-a\,a)$ admits spectral synthesis. Sev
eral years ago\nA. Baranov\, A. Borichev and myself managed to give a nega
tive answer to this question which implies\,\nin particular\, that there e
xist non-harmonic Fourier series which do not admit a linear\nsummation me
thod. We also showed that any exponential system admits the\nsynthesis up
to a one-dimensional defect. Apart from this\, I will discuss related prob
lems\nfor systems of reproducing kernels in Hilbert spaces of entire funct
ions. In particular\,\nI will talk about a counterexample to the Newman-Sh
apiro conjecture posed in 1966 \n(joint work with A. Borichev).\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yilong Wang
DTSTART:20240828T073000Z
DTEND:20240828T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/54
DESCRIPTION:Title: Alterfold invariants and alterfold TQFT\nby Yilong Wang a
s part of Moscow-Beijing topology seminar\n\n\nAbstract\nIn this talk\, we
introduce the notion of alterfold invariants and their associated TQFTs.
Then we will give several applications including the topological descripti
on of the Drinfeld center\, the equivalence between the RT- and TV-TQFTs\,
and the equivariance of the generalized Frobenius-Schur indicators. Final
ly\, we will discuss how to obtain families of Morita invariants as genera
lizations of the indicators\, and speculate some of the potential applicat
ions. This is based on joint work with Zhengwei Liu\, Shuang Ming and Jins
ong Wu.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arkadiy Skopenkov
DTSTART:20240821T073000Z
DTEND:20240821T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/55
DESCRIPTION:Title: The band connected sum and the second Kirby move for higher-d
imensional links\nby Arkadiy Skopenkov as part of Moscow-Beijing topol
ogy seminar\n\n\nAbstract\nLet $f:S^q\\sqcup S^q\\to S^m$ be an (ordered o
riented) link (i.e. an embedding).\n\nHow does (the isotopy class of) the
knot $S^q\\to S^m$ obtained by embedded connected sum of the components of
$f$ depend on $f$?\n\nDefine a link $\\sigma f:S^q\\sqcup S^q\\to S^m$ as
follows.\nThe first component of $\\sigma f$ is the `standardly shifted'
first component of $f$.\nThe second component of $\\sigma f$ is the embedd
ed connected sum of the components of $f$.\nHow does (the isotopy class of
) $\\sigma f$ depend on $f$?\n\nHow does (the isotopy class of) the link $
S^q\\sqcup S^q\\to S^m$ obtained by embedded connected sum of the last two
components of a link $g:S^q_1\\sqcup S^q_2\\sqcup S^q_3\\to S^m$ depend o
n $g$?\n\nWe give the answers for the `first non-trivial case' $q=4k-1$ an
d $m=6k$.\nThe first answer was used by S. Avvakumov for classification of
linked 3-manifolds in $S^6$.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shuang Ming (BIMSA)
DTSTART:20240807T073000Z
DTEND:20240807T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/56
DESCRIPTION:Title: Tensor categories and alterfold theory\nby Shuang Ming (B
IMSA) as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIn this ta
lk\, I will introduce a partition function defined on bi-colored three-man
ifolds decorated by tensor diagrams from a spherical fusion category \\mat
hcal{C}. We called them 3 dimensional alterfold. This partition function y
ields three-manifold invariants and three-dimensional topological quantum
field theories (TQFTs). I will discuss how well-known invariants and TQFTs
\, such as Turaev-Viro theory and Reshetikhin-Turaev theory\, can be natur
ally embedded within our framework. Furthermore\, our bi-colored theory pr
ovides topological interpretations for fundamental concepts in tensor cate
gories\, including the Drinfeld center and Frobenius-Schur indicators. We
expect the theory could generalizes to higher dimensions\, and could produ
ce new identities for (higher) tensor categories.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhengwei Liu
DTSTART:20240911T073000Z
DTEND:20240911T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/57
DESCRIPTION:by Zhengwei Liu as part of Moscow-Beijing topology seminar\n\n
Abstract: TBA\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jie Wu
DTSTART:20241009T073000Z
DTEND:20241009T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/58
DESCRIPTION:Title: Topology meets Artificial Intelligence (AI)\nby Jie Wu as
part of Moscow-Beijing topology seminar\n\n\nAbstract\nThis talk aims to
address one of the fundamental questions in the mind of youngth what we (a
s topologists or pre-topologists) could/should do in the times of Artifici
al Intelligence (AI). For helping you to find the answer of this question
that is suitable to yourself\, we will talk by samples on the bi-direction
al interactions between algebraic topology and AI\, which consists of an i
ntroduction to a work of Kirill Brilliantov\, Fedor Pavutniskiy\, Dmitry P
asechnyuk and German Magao on the applications of language models to some
hard problems in algebraic topology\, a new-born research field of GLMY th
eory on digraphs that aims to establish topological foundations for high-o
rder interaction complex network\, and some practical applications of alge
braic topology in sciences.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bing Fang (Dalian University of Technology)
DTSTART:20240904T073000Z
DTEND:20240904T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/59
DESCRIPTION:Title: Sufficient conditions for amalgamated 3-manifolds to be $\\pa
rtial$-irreducible and irreducible\nby Bing Fang (Dalian University of
Technology) as part of Moscow-Beijing topology seminar\n\n\nAbstract\nLet
$M=M_1\\cup_F M_2$ be an amalgamation of two 3-manifolds $M_1$ and $M_2$
along a compact connected surface $F$. In this talk\, we first give some s
ufficient conditions for $M$ to be $\\partial$-irreducible in terms of dis
tances between certain vertex subsets of the curve complex $C(F)$ and the
arc complex $A(F)$. Then we introduce the extended curve complex $\\wideti
lde{C}(F)$ of a compact connected surface $F$. In the case that $F$ is bi-
compressible in the amalgamated 3-manifold $M$ and in the case that $F$ is
compressible only in one of $M_1$ and $M_2$\, we give some sufficient con
ditions in terms of distance between some vertex subsets of $\\widetilde{C
}(F)$ for $M$ to be irreducible\, respectively.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexis Verelzier
DTSTART:20241002T073000Z
DTEND:20241002T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/60
DESCRIPTION:Title: State sum homotopy invariants of maps\nby Alexis Verelzie
r as part of Moscow-Beijing topology seminar\n\n\nAbstract\nHomotopy quant
um field theories (HQFTs) generalize topological quantum field theories (T
QFTs). The idea is to use TQFT techniques to study principal fiber bundles
over manifolds and\, more generally\, homotopy classes of maps from manif
olds to a fixed target space X. In particular\, such an HQFT induces a sca
lar invariant of homotopy classes of maps from closed manifolds to X. It i
s well-known that groups are algebraic models for 1-types. Generalizing gr
oups\, crossed modules model 2-types. In this talk\, I will explain how to
generalize the Turaev-Viro-Barett-Westburry state sum method to define a
3-dimensional HQFT with target X in the following two cases: first when X
is a 1-type using fusion categories graded by a group (joint work with Vla
dimir Turaev) and second when X is a 2-type using fusion categories graded
by a crossed module (joint work with Kursat Sozer).\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liliya Grunwald
DTSTART:20240918T073000Z
DTEND:20240918T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/61
DESCRIPTION:Title: Аналитическая теория циркулянтн
ых графов и ее приложения к комбинаторно
му анализу\nby Liliya Grunwald as part of Moscow-Beijing topo
logy seminar\n\n\nAbstract\nДоклад посвящен изучению
актуальных вопросов современного анали
за\, которые находятся на стыке комплекс
ного анализа\, комбинаторного анализа\, т
еории графов и алгебры. В работе рассмат
риваются спектральные и алгебраические
свойства дискретного лапласиана\, приме
нительно к широкому семейству циркулянт
ных графов и их различных обобщений.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20240925T073000Z
DTEND:20240925T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/62
DESCRIPTION:Title: Classification of knots in $S_{g} \\times S^{1}$ with small n
umber of crossings\nby Seongjeong Kim as part of Moscow-Beijing topolo
gy seminar\n\n\nAbstract\nIn knot theory not only classical knots\, which
are embedded circles in S^{3} up to isotopy\, but also knots in other 3-ma
nifolds are interesting for mathematicians. In particular\, virtual knots\
, which are knots in thickened surface $S_{g} \\times [0\,1]$ with an orie
ntable surface $S_{g}$ of genus $g$\, are studied and they provide interes
ting properties.\n\nIn this talk\, we will talk about knots in $S_{g} \\ti
mes S^{1}$ where $S_{g}$ is an oriented surface of genus $g$. We introduce
basic notions and properties for them. In particular\, for knots in $S_{g
} \\times S^{1}$ one of important information is “how many times a half
ot a crossing turns around $S^{1}$”\, and we call it winding parity of a
crossing. We extend this notion more generally and introduce a topologica
l model. In the end we apply it to classify knots in $S_{g}\\times S^{1}$
with small number of crossings.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peng Du
DTSTART:20241016T073000Z
DTEND:20241016T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/63
DESCRIPTION:Title: Isotropic points in the Balmer spectrum of stable motivi
c homotopy categories\nby Peng Du as part of Moscow-Beijing topology s
eminar\n\n\nAbstract\nI will discuss the tensor-triangulated geometry of t
he stable motivic homotopy category SH(k) and a big family of the so-cal
led isotropic realisation functors\, parameterized by the choices of a M
orava K-theory and an extension of the base field k (of characteristic
zero). By studying the target category of such an isotropic realisatio
n functor\, we are able to construct the so-called isotropic Morava poi
nts of the Balmer spectrum Spc(SH(k)^c) of the stable motivic homotopy
category SH(k). This is based on joint work with Alexander Vishik.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Y. Vesnin
DTSTART:20241023T073000Z
DTEND:20241023T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/64
DESCRIPTION:Title: Polynomials of complete spatial graphs and Jones polynomials
of related links\nby Andrey Y. Vesnin as part of Moscow-Beijing topolo
gy seminar\n\n\nAbstract\nSpatial graphs are embeddings of graphs in thre
e-dimensional space. With each spatial graph one can relate constituent k
nots formed by embeddings of cycles. The study of spatial graphs uses bot
h combinatorial and topological methods.\nDenote by K4 a complete graph
with four vertices. We will discuss spatial K4-graphs and related knots a
nd links. We will present formular connecting normalized Yamada polynomia
l of a spatial K4-graph and Jones polynomials of a collection of knots an
d links related.\nThe talk is based on a joint work with Olga Oshmarina\,
see arXiv:2404:12264.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hayato Imori
DTSTART:20241030T073000Z
DTEND:20241030T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/65
DESCRIPTION:Title: Instantons\, Khovanov homology\, and immersed cobordism maps<
/a>\nby Hayato Imori as part of Moscow-Beijing topology seminar\n\n\nAbstr
act\nThe functorial properties of homological knot invariants have provide
d powerful tools for studying low-dimensional objects. Khovanov homology a
nd singular instanton Floer homology are such homological knot invariants.
Kronheimer and Mrowka constructed a spectral sequence that links Khovanov
homology and a version of singular instanton Floer homology\, demonstrati
ng that Khovanov homology can detect the unknot. In this talk\, we will sh
ow that Kronheimer-Mrowka's spectral sequence relates cobordism maps in Kh
ovanov homology theory and instanton Floer theory. Furthermore\, our const
ruction includes induced maps for immersed cobordisms between knots. This
result also has topological applications related to knot concordance and e
xotic phenomena of immersed surfaces in 4-manifolds. This talk is based on
joint work with Taketo Sano\, Kouki Sato\, and Masaki Taniguchi.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rama Mishra
DTSTART:20241120T073000Z
DTEND:20241120T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/66
DESCRIPTION:Title: Parameterizing Real rational knots by Gluing\nby Rama Mis
hra as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIn this talk
we discuss that knots in real projective three space can be parametrized
by embedding given by homogeneous polynomials of same degree.\nSuch knots
are referred as real rational knots. We show that the problem of construc
ting a real rational knot of a reasonably low degree can be reduced to an
algebraic problem involving the pure braid group: expressing an associated
element of the pure braid group in terms of the standard generators of th
e pure braid group. If time permits we also predict the existence of a rea
l rational knot in a degree that is expressed in terms of the edge number
of its polygonal representation.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fyodor Ivlev
DTSTART:20241106T073000Z
DTEND:20241106T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/67
DESCRIPTION:Title: The boundness of distance between two sets of fixed volume in
side the multidimensional right figures of unite volume.\nby Fyodor Iv
lev as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIf we consid
er the diameter of unit multidimensional cube it tends to the infinity whe
n the number of the dimensions of the cube tends to infinity. But what wou
ld be if we consider the distance between to sets of the fixed (but small)
volumes instead of the distance between two point\, whose volumes are equ
al to 0? The Theorem is proven that this distance is bounded by a constant
not depending of the dimensions of the cube\, only by the initial volumes
of the sets. The similar question about the sphere or other right figures
(instead of the cube) are also considered. There are asymptotic approxima
tions of the limits of the maximum possible distance between such sets are
given. For some figures the case of convex sets is considered more precis
e.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bao Vuong
DTSTART:20241113T073000Z
DTEND:20241113T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/68
DESCRIPTION:Title: A personal journey along Alexander polynomials\nby Bao Vu
ong as part of Moscow-Beijing topology seminar\n\n\nAbstract\nI will talk
about somewhat a memorial story of my study about Alexander polynomials\,
what I have learned\, what I would want to understand. Along the way I got
some elementary results on Alexander polynomials of links in Poincare hom
ology sphere\, a work in progress on Fox-Milnor condition for knot concord
ance in Poincare homology sphere.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg N. German
DTSTART:20241127T073000Z
DTEND:20241127T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/69
DESCRIPTION:Title: Theorems of Dirichlet\, Vahlen\, and Hurwitz\nby Oleg N.
German as part of Moscow-Beijing topology seminar\n\n\nAbstract\nWe will d
iscuss some very simple yet elegant results that\, in various ways\, stren
gthen Dirichlet's theorem on the approximation of real numbers by rational
s. Both arithmetic proofs and geometric ones will be considered\, includin
g those employing Klein polygons—a geometric interpretation of continued
fractions.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miztani Euich
DTSTART:20241204T073000Z
DTEND:20241204T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/70
DESCRIPTION:Title: Time-independent Special Theory of Relativity\nby Miztani
Euich as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIn the pr
ocess of Albert Einstein establishing the theory of special relativity\, t
he principle of relativity is completely based on a geometrical descriptio
n. On the other hand\, the electro-magnetic theory is purely algebraic and
complicated. Minkowski’s work extended it for 4-dimensional space-time
which is purely algebraic as well. \n\nHowever\, we can understand Einstei
n's ideas much simpler and more phenomenally in section 1. Such a descript
ion of special relativity will facilitate research in spintronics to consi
der the relativistic effect. Besides\, it leads to an unknown special orth
ogonal group in real space\, not the indefinite orthogonal group SO(1\,3)
in section 2. Furthermore\, long-standing controversies of displacement cu
rrent will be solved in section 3. In this talk we discuss the ‘complete
’ geometric special relativity and its new Lie group in real space.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weibiao Wang
DTSTART:20241211T073000Z
DTEND:20241211T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/71
DESCRIPTION:Title: Embeddability of non-orientable closed surfaces in 3-manifold
s\nby Weibiao Wang as part of Moscow-Beijing topology seminar\n\n\nAbs
tract\nWe know that non-orientable closed surfaces can not be embedded in
the 3-sphere. Naturally\, we ask for a given 3-manifold which non-orientab
le closed surfaces can be embedded in it. For any lens space\, or the prod
uct of any surface and the circle\, the answer is known\, mainly by the wo
rk of Bredon and Wood\, as well as those of Jaco\, End\, Rannard\, and so
on. I will review their results\, and then discuss embeddability of non-or
ientable closed surfaces in surface bundles over the circle. For the total
space of any torus bundle over the circle\, we determine the genera of no
n-orientable closed surfaces that can be embedded in it. This is joint wor
k with Xiaoming Du and Yimu Zhang.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhengyi Zhou
DTSTART:20241218T073000Z
DTEND:20241218T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/72
DESCRIPTION:Title: Kahler compactification of C^n and Reeb dynamics\nby Zhen
gyi Zhou as part of Moscow-Beijing topology seminar\n\n\nAbstract\nWe will
present two results in complex geometry: (1) A Kahler compactification of
C^n with a smooth divisor complement must be P^n\, which confirms a conje
cture of Brenton and Morrow(1978) under the Kahler assumption\; (2) Any co
mplete asymptotically conical Calabi-Yau metric on C^3 with a smooth link
must be flat\, confirming a modified version of Tian’s conjecture regard
ing the recognition of the flat metric among Calabi-Yau metrics in dimensi
on 3. Both proofs rely on relating the minimal discrepancy number of a Fan
o cone singularity to its Reeb dynamics of the conic contact form. This is
a joint work with Chi Li.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gu Xing
DTSTART:20241225T073000Z
DTEND:20241225T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/73
DESCRIPTION:Title: Polynomial invariants and the cohomology of $BPU(p^m)$\nb
y Gu Xing as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIn thi
s talk\, invariant polynomials refer to polynomials over a prime field of
positive characteristics that are invariant under some group actions. We r
eveal several connections between invariant polynomials and the cohomology
of $BPU(p^m)$\, the classifying space of the projective unitary group $PU
(p^m)$ where $p$ is an odd prime number.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Bludov
DTSTART:20250108T073000Z
DTEND:20250108T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/74
DESCRIPTION:Title: Balanced sets and homotopy invariants of covers\nby Mikha
il Bludov as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIt is
known that any covering of an $m$-dimensional sphere $S^m$ by $n \\geq 2$
open (or closed) sets can be associated with a homotopy class of maps from
$S^m$ to $S^{n-2}$. We show that by considering certain $n$ points in Euc
lidean space $\\mathbb{R}^d$\, this covering of the sphere $S^m$ can also
be associated with a homotopy class of maps from $S^m$ to $S^{d-1}$. In th
e case $S^m = \\partial D^{m+1}$\, the resulting homotopy class\, when non
trivial\, acts as an obstruction to certain extensions of the covering to
the entire disk $D^{m+1}$. Using this\, we derive the KKMS lemma\, as well
as its analogues and generalizations. We also show that modulo an automor
phism of order 2 on the homotopy group\, the homotopy class of the coverin
g does not depend on the choice of the set of points in $\\mathbb{R}^d$\,
provided that these sets are balancedly equivalent.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arina Filimonova
DTSTART:20250115T073000Z
DTEND:20250115T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/75
DESCRIPTION:Title: Morphisms generating Lyndon words\nby Arina Filimonova as
part of Moscow-Beijing topology seminar\n\n\nAbstract\nWe will discuss th
e problem of characterizing morphisms that generate Lyndon words. This pro
blem has been solved for the binary alphabet (Richomme\, Séébold (2021))
\, but for obvious reasons\, the obtained result can not be generalized to
alphabets of larger sizes. We will review the original result and then di
scuss the possibility of reformulating it in a way that allows generalizat
ion to larger alphabets. We will also discuss some potential approaches to
achieving this generalization.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Euich Miztani
DTSTART:20250122T073000Z
DTEND:20250122T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/76
DESCRIPTION:Title: Time-independent Special Theory of Relativity\nby Euich M
iztani as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIn the pr
ocess of Albert Einstein establishing the theory of special relativity\, t
he principle of relativity is completely based on a geometrical descriptio
n. On the other hand\, the electro-magnetic theory is purely algebraic and
complicated. Minkowski’s work extended it for 4-dimensional space-time
which is purely algebraic as well. However\, we can understand Einstein's
ideas much simpler and more phenomenally in section 1. Such a description
of special relativity will facilitate research in spintronics to consider
the relativistic effect. Besides\, it leads to an unknown special orthogo
nal group in real space\, not the indefinite orthogonal group SO(1\,3) in
section 2. Furthermore\, long-standing controversies of displacement curre
nt will be solved in section 3. In this talk we discuss the ‘complete’
geometric special relativity and its new Lie group and Lorentz covariance
in real space.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mohammed Sabak
DTSTART:20250129T073000Z
DTEND:20250129T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/77
DESCRIPTION:by Mohammed Sabak as part of Moscow-Beijing topology seminar\n
\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Zheglov
DTSTART:20250312T073000Z
DTEND:20250312T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/78
DESCRIPTION:Title: String equation in the ring of differential operators and the
Dixmier conjecture for the first Weyl algebra\nby Alexander Zheglov a
s part of Moscow-Beijing topology seminar\n\n\nAbstract\nI will talk about
the correspondence between the solutions of the string equation [P\,Q]=1
in the ring of differential operators (and in particular\, in the first We
yl algebra) and pairs of commuting ordinary differential operators of rank
one. The solutions of the string equation in the first Weyl algebra descr
ibe all its endomorphisms\, and thus it is possible to obtain conditions t
hat single out endomorphisms that are not automorphisms (the Dixmier conje
cture for the first Weyl algebra).\n The indicated correspondence is appli
ed to the proof of the Dixmier conjecture\, the outline of which I will tr
y to present in the talk. The proof is also based on the theory of normal
forms for ordinary differential operators and the technique of Newton poly
gons for the first Weyl algebra.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiyun Cheng (Beijing Normal University)
DTSTART:20250219T073000Z
DTEND:20250219T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/79
DESCRIPTION:Title: The construction of topological biquandles\nby Zhiyun Che
ng (Beijing Normal University) as part of Moscow-Beijing topology seminar\
n\n\nAbstract\nA biquandle is a set equipped with two binary operations\,
which provides a set-theoretic solution of the Yang-Baxter equation. A top
ological biquandle is a topological space with a compatible biquandle stru
cture. In this talk\, I will give a quick introduction to quandle theory a
nd then explain how to construct some nontrivial examples of topological b
iquandles.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Melikhov
DTSTART:20250226T073000Z
DTEND:20250226T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/80
DESCRIPTION:Title: n-Quasi-isotopy and its applications\nby Sergey Melikhov
as part of Moscow-Beijing topology seminar\n\n\nAbstract\n0-Quasi-isotopy
is just another name for link homotopy\, and the relations of k-quasi-isot
opy\, where k is a positive \ninteger\, are equivalence relations on PL (o
r smooth) links which are higher-order analogues of link homotopy\, retain
ing \nsome key geometric properties of link homotopy. k-Quasi-isotopy is c
losely related to type k invariants of links\, to Milnor's \n\\bar\\mu-inv
ariants with at most k+1 occurrences of each index and to the first k+1 po
tentially nonzero coefficients of \nthe Conway polynomial\, as well as to
self C_{k+1}-equivalence\, (k+1)-cobordism of Cochran and Orr\, and class
k+1 \ngrope cobordism of Cochran\, Orr and Teichner. (The details\, at lea
st some of them\, will be reviewed in the talk.) In fact \nthe filtration
extends to half-integer k\, and it turns out in particular that 0.5-quasi-
isotopy coincides with \\Delta-link homotopy \n(also known as self C_2-equ
ivalence).\n\nThe main applications of k-quasi-isotopy are to the relation
s of PL and topological isotopy. In particular\, if two PL links are \ntop
ologically isotopic (=homotopic through embeddings)\, then they are k-quas
i-isotopic for all k\; and if they are \nk-quasi-isotopic for all k\, then
they are PL isotopic (=equivalent up insertion and deletion of local knot
s) to a pair of PL links \nwhich are not separated by finite type invarian
ts. Thus D. Rolfsen's 1974 problem: "if two PL links are topologically iso
topic\, \nare they PL isotopic?" is solved affirmatively modulo the well-k
nown conjecture that PL links are separated by finite type \ninvariants. A
mong other applications of k-quasi-isotopy are partial results on another
1974 problem of Rolfsen: "is every \n(topological) knot isotopic to the un
knot?" \n\nThe applications to isotopy are mostly new\, and were the main
focus of a number of my recent talks\, including the ones at \nthe Beijing
-Moscow Mathematics Colloquium and the 10th Russia-China Conference of Kno
t Theory and Related Topics. \nBy contrast\, the present talk will mostly
focus on k-quasi-isotopy itself\, for a fixed k\, and review results and o
pen problems\nthat are mostly old (dating to 20-25 years ago) but seem to
still interest some people.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Антон Белецкий
DTSTART:20250212T073000Z
DTEND:20250212T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/81
DESCRIPTION:Title: Итеративная теория малых сокраще
ний И. Рипса и ее применение к проблеме
Бернсайда\nby Антон Белецкий as part of Moscow-B
eijing topology seminar\n\n\nAbstract\nПроблема Бернсайда
широко известна как один из важнейших в
опросов теории групп. Ключевой областью
\, позволившей достичь успехов в ее реше
нии\, стала так называемая теория малых
сокращений\, изучающая группы\, образующ
ие соотношения в которых слабо пересека
ются друг с другом (обощения этой теори
и используются в классической работе С.
И. Адяна и П. С. Новикова\, а также в работ
ах А. Ю. Ольшанского)\nВ докладе будет опи
сано альтернативное построение градуир
ованной теории малых сокращений\, разра
ботанное И. Рипсом. Мы постараемся геоме
трически исследовать свойства диаграмм
Ван Кампена в группах\, где соотношения
схожих размеров слабо зацепляются друг
за друга\, и продемонстрируем применим
ость этой теории для анализа групп Бернс
айда. Желательно предварительное знако
мство с основными идеями теории малых с
окращений (вплоть до леммы Гриндлингера)
\, однако необходимые определения и моти
вировки будут кратко даны в процессе док
лада.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valeriy Bardakov
DTSTART:20250305T073000Z
DTEND:20250305T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/82
DESCRIPTION:Title: Multi-virtual braid groups and their representations\nby
Valeriy Bardakov as part of Moscow-Beijing topology seminar\n\n\nAbstract\
nIn this talk we discuss multi-virtual braid groups and symmetric multi-vi
rtual braid groups which were introduced by Prof. Kauffman in 2024. We de
ne two normal subgroups of finite index subgroups of multi-virtual brai
d groups. Also\, we construct representations of multi-virtual braid group
s by automorphisms of some groups. At the end we give an answer on a quest
ion of Prof. Kau man on non-triviality of 2-multi-virtual knots.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eiji Ogasa
DTSTART:20250402T073000Z
DTEND:20250402T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/83
DESCRIPTION:Title: Are all 2-dimasional links in the 4-sphere slice?\nby Eij
i Ogasa as part of Moscow-Beijing topology seminar\n\n\nAbstract\nAre all
2-dimasional links in the 4-sphere slice?\nIt is an outstanding open quest
ion.\nWe introduce the speaker's partial solution and his related results.
\nWe talk about terminologies and history of this important question.\nWe
discuss other dimensional version of this question and the speaker's resul
ts.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Satoshi Nawata
DTSTART:20250319T083000Z
DTEND:20250319T100000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/84
DESCRIPTION:Title: Skein algebras and DAHA\nby Satoshi Nawata as part of Mos
cow-Beijing topology seminar\n\n\nAbstract\nI will talk about the represen
tation theory of double affine Hecke algebras in terms of brane quantizati
on on SL(2\,C)-character variety of a Riemann surface. In addition\, I wil
l explain the relation between DAHA and skein algebras\, and the relation
to modular tensor categories.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Satoshi Nawata
DTSTART:20250326T073000Z
DTEND:20250326T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/85
DESCRIPTION:Title: Skein algebras and DAHA\nby Satoshi Nawata as part of Mos
cow-Beijing topology seminar\n\n\nAbstract\nI will talk about the represen
tation theory of double affine Hecke algebras in terms of brane quantizati
on on SL(2\,C)-character variety of a Riemann surface. In addition\, I wil
l explain the relation between DAHA and skein algebras\, and the relation
to modular tensor categories.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Chernov
DTSTART:20250409T073000Z
DTEND:20250409T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/86
DESCRIPTION:Title: Virtual Legendrian knots\, generalized Manturov projection an
d corollaries\nby Vladimir Chernov as part of Moscow-Beijing topology
seminar\n\n\nAbstract\nVirtual Legendrian knots were introduced by Cahn an
d Levi and they are Legendrian knots in spherical cotangent bundles of clo
sed surfaces up to isotopy\, stabilization and destabilization of a surfac
e away from the front projection of the knot. The talk is based on joint r
esults with Sadykov. We briefly review Kuperberg type theorem for virtual
Legendrian knots and their applications to the study of causality in Borde
Sorkin spacetimes. We construct the generalization of Manturov projection
to such knots and apply this to the study of canonical genus and k-arc cr
ossing number for such knots.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanghzhou Liu
DTSTART:20250416T073000Z
DTEND:20250416T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/87
DESCRIPTION:Title: On the Burau & Lawrence-Krammer-Bigelow's representation\
nby Yanghzhou Liu as part of Moscow-Beijing topology seminar\n\n\nAbstract
\nThere are many interesting question:\n\n- How to map a braid to a matrix
?\n- What's the topology meaning of the representation?\n- Is the represen
tations faithful?\n\nAs Prof. Manturov's the book said\, the basic and the
key lemma are very important for the 3rd point. So why are they true? Thi
s question allow us to explore the 2nd point. In fact\, it is very beautif
ul construction.\n\nToday\, I will introduce some necessary details about
this topic: Burau & Lawrence-Krammer-Bigelow's representation.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miztani Euich
DTSTART:20250423T100000Z
DTEND:20250423T113000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/88
DESCRIPTION:Title: How Should We Interpret Space Dimension? — Trial for a Math
ematical Foundation in Higher Dimensional Physics\nby Miztani Euich as
part of Moscow-Beijing topology seminar\n\n\nAbstract\nIn modern physics
we could say that space dimension is derived from physical conditions. Kal
uza-Klein theory and D-brane are typical examples. However\, not only by s
uch conditions\, we should also think about space dimension with insights
from known facts without any physical conditions. In this talk we rethink
space dimensionality from scratch.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Taranenko
DTSTART:20250507T073000Z
DTEND:20250507T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/89
DESCRIPTION:Title: Transversals in iterated quasigroups and latin hypercubes of
order 4\nby Anna Taranenko as part of Moscow-Beijing topology seminar\
n\n\nAbstract\nA latin hypercube of order n is a multidimensional array fi
lled with n symbols such that each line contains all n symbols. A transver
sal in latin hypercube is a diagonal that contains all distinct symbols. G
iven a binary quasigroup G of order n\, let the d-iterated quasigroup G[d]
be the (d+1)-dimensional latin hypercube equal to the Cayley table of G c
omposed with itself d times. In this talk\, we characterize latin hypercub
es of order 4 that do not have transversals and describe a method for coun
ting transversals in iterated quasigroups.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20250430T073000Z
DTEND:20250430T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/90
DESCRIPTION:Title: Group $G_{n}^{3}$ with oriented triple points and braid invar
iant\nby Seongjeong Kim as part of Moscow-Beijing topology seminar\n\n
\nAbstract\nIn 2015 the group $G_{n}^{3}$ is defined by V.O. Manturov. By
V.O. Manturov and I.M. Nikonov\, it is shown that there exists a well-defi
ned map from braid group to $G_{n}^{3}$ taking triple points.\nIn this tal
k\, we talk about modifications of group $G_{n}^{3}$ by determining order
of triple points on a line. We construct an invariant for pure braids by u
sing the modified $G_{n}^{3}$ and provide an example\, which could not be
distinguished with trivial braids by using $G_{n}^{3}$. In the end of talk
\, we discuss on further research.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Carter
DTSTART:20250514T073000Z
DTEND:20250514T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/91
DESCRIPTION:Title: Braiding and Folding Branched Covers of the 3-sphere.\nby
Scott Carter as part of Moscow-Beijing topology seminar\n\n\nAbstract\nGi
ven a knot or a link in the 3-dimensional sphere\, we consider branched co
vers of the 3-sphere that are branched over the knot. The branched covers
are manufactured from the unbranched irregular covers of the knot compleme
nt which are associated to homomorphisms of the fundamental group. The bra
nched covers can often be mapped into a tropical region of the 4-dimension
al sphere in such a way that the projection onto an equatorial 3-sphere in
duces the branched cover. We will present several examples of such folding
and indicate how they can be constructed in general.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangzhou LIU
DTSTART:20250521T073000Z
DTEND:20250521T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/92
DESCRIPTION:Title: From Knot Groups to Alexander Polynomial: A Non-standard Algo
rithm\nby Yangzhou LIU as part of Moscow-Beijing topology seminar\n\n\
nAbstract\nThis presentation is divided into two parts. First\, we review
the algebraic topology picture and significance of the Alexander polynomia
l\, from which we can obtain the "standard algorithm" for getting from kno
t groups to the Alexander polynomial. In the second part\, I will share a
phenomenon discovered by Mr. Mingli Yuan\, which I personally call the "no
n-standard algorithm" (compared to the above "standard algorithm"). After
a large number of experimental verifications by Yuan\, it works for many k
nots. Specifically\, if a knot group is generated by two generators and ha
s one relation\, i.e.\, \\( G = \\langle x\, y | R \\rangle \\)\, then whe
n \\( R \\) satisfies certain relations\, a very simple algorithm for obta
ining the Alexander polynomial from it will be achieved: here\, \\( x \\)
represents the +1 operation\, and \\( y \\) represents the ×t operation.
Thus\, treating \\( R \\) as a string of instructions acting from right to
left\, \\( R(x) = x \\)\, and the expansion then gives the Alexander poly
nomial.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Завесов Александр Львович
DTSTART:20250528T073000Z
DTEND:20250528T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/93
DESCRIPTION:Title: Теория соседства\nby Завесов Але
ксандр Львович as part of Moscow-Beijing topology seminar\n\n
Abstract: TBA\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kensuke Arakawa
DTSTART:20250611T073000Z
DTEND:20250611T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/94
DESCRIPTION:Title: Monoidal relative categories model monoidal (∞\,1)-categori
es\nby Kensuke Arakawa as part of Moscow-Beijing topology seminar\n\n\
nAbstract\nThis is a talk on higher category theory\, aimed at topologists
in a broad sense. No prior experience with higher categories will be assu
med.\n\nHomotopical study of mathematical objects often starts by identify
ing a subcategory of "weak equivalences" that behave like isomorphisms. In
this spirit\, relative categories offer a minimalistic framework for homo
topy theory: They are categories equipped with a designated subcategory of
weak equivalences. A remarkable theorem of Barwick and Kan shows that thi
s simple structure in fact models (∞\,1)-categories. More precisely\, an
y relative category (C\,W) gives rise to an (∞\,1)-category C[W^{-1}] by
localizing at the weak equivalences. This process defines a functor\nRelC
at[DK^{-1}]-->Cat_{(∞\,1)}\,\nwhere DK denotes the subcategory of relati
ve functors that induce equivalences of localizations. Barwick and Kan sho
wed that this functor is an equivalence.\n\nIn practice\, many relative ca
tegories come equipped with a monoidal structure whose tensor product pres
erves weak equivalences in each variable. In such cases\, the localization
inherits a monoidal structure. This raises a natural question: Do monoida
l relative categories model monoidal (∞\,1)-categories? The author recen
tly proved that the answer is yes\, borrowing techniques inspired by Segal
's infinite loop space machine. In this talk\, we explain the ideas behind
the proof\, explore some applications\, and suggest possible generalizati
ons.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fengling Li
DTSTART:20250604T073000Z
DTEND:20250604T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/95
DESCRIPTION:Title: A three-variable invariant of planar knotoids\nby Fenglin
g Li as part of Moscow-Beijing topology seminar\n\n\nAbstract\nAs a genera
lization of the classical knots\, knotoids are equivalence classes of imme
rsions of the oriented unit interval in a surface. In recent years\, a va
riety of invariants of spherical and planar knotoids have been constructed
as extensions of invariants of classical and virtual knots. In this talk\
, we introduce a three-variable transcendental invariant of planar knotoid
s which is defined over an index function of a Gauss diagram. We describe
properties of this invariant and show that it is a Vassiliev invariant of
order one. We provide lower bounds on the Gordian distance of homotopic pl
anar knotoids by using the transcendental invariant. This is joint work wi
th Wandi Feng and Andrei Vesnin.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arunima Ray
DTSTART:20250618T073000Z
DTEND:20250618T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/96
DESCRIPTION:Title: Constructing locally flat surfaces in 4-manifolds (part 1)\nby Arunima Ray as part of Moscow-Beijing topology seminar\n\n\nAbstract
\nThere are two main approaches to building locally flat surfaces in 4-man
ifolds: direct methods applying Freedman-Quinn's disc embedding theorem\,
and indirect methods using surgery theory. (Notably the second method also
requires the disc embedding theorem\, but only indirectly.) In this seque
nce of two lectures\, I will give an introduction to both methods. In this
first lecture I will give a direct\, constructive proof of a result of Le
e-Wilczynski which states that every primitive second homology class in a
closed\, simply connected 4-manifold is represented by a locally flat toru
s.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arunima Ray
DTSTART:20250625T073000Z
DTEND:20250625T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/97
DESCRIPTION:Title: Constructing locally flat surfaces in 4-manifolds (part 2)\nby Arunima Ray as part of Moscow-Beijing topology seminar\n\n\nAbstract
\nThere are two main approaches to building locally flat surfaces in 4-man
ifolds: direct methods applying Freedman-Quinn's disc embedding theorem\,
and indirect methods using surgery theory. (Notably the second method also
requires the disc embedding theorem\, but only indirectly.) In this seque
nce of two lectures\, I will give an introduction to both methods. In this
second lecture I will give a surgery-theoretic proof of a result of Freed
man-Quinn\, which states that every Alexander polynomial one knot is topol
ogically slice.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frolov Aleksandr
DTSTART:20250709T073000Z
DTEND:20250709T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/98
DESCRIPTION:Title: Motivic Knots and the Abhyankar-Moh Conjecture\nby Frolov
Aleksandr as part of Moscow-Beijing topology seminar\n\n\nAbstract\nThe A
bhyankar-Moh theorem in affine algebraic geometry states that any polynomi
al embedding i:\\mathbb{C}\\hookrightarrow\\mathbb{C}^3 can be rectified.
This means there exists a polynomial automorphism f of \\mathbb{C}^3 such
that f\\circ i = t \\mapsto (t\, 0\, 0).\n\nThe Abhyankar-Moh conjecture g
eneralizes this idea: It proposes that any polynomial embedding \\mathbb{C
}^k\\hookrightarrow\\mathbb{C}^n can be rectified\, for all dimensions k a
nd n. While this is known to hold when n > 2k + 1\, the conjecture remains
open even for specific cases. For example\, it is unsolved for the embedd
ing \\mathbb{C}\\hookrightarrow\\mathbb{C}^3 : t \\mapsto (t^3-3t\, t^4-4t
^2\, t^5-10t).\n\nA promising approach to this conjecture uses techniques
from geometric topology\, especially knot theory. Recent research explores
how Morel-Voevodsky’s motivic homotopy theory can bridge topological me
thods and algebraic geometry\, offering new strategies for such problems.\
n\nIn this talk\, I will overview the basics of modern algebraic geometry
and motivic homotopy theory. The goal is to introduce motivic knots and th
eir invariants. Familiarity with commutative algebra and category theory i
s assumed.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eiji Ogasa
DTSTART:20250723T073000Z
DTEND:20250723T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/99
DESCRIPTION:by Eiji Ogasa as part of Moscow-Beijing topology seminar\n\nAb
stract: TBA\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takuya Sakasai
DTSTART:20250716T073000Z
DTEND:20250716T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/100
DESCRIPTION:Title: On the structure of groups defined by Kim and Manturov\n
by Takuya Sakasai as part of Moscow-Beijing topology seminar\n\n\nAbstract
\nWe consider a series of groups $\\Gamma_n^4$ defined by Kim and Manturov
. These groups have their background in Delaunay triangulations of a plane
and they are expected to have relationships to many geometric objects. In
this talk\, by a group theoretical argument\, we show that the groups $\\
Gamma_n^4$ are finite for all n $\\ge 6$ and in fact they are 2-step nilpo
tent 2-groups.\nThis is a joint work with Carl-Fredrik Nyberg-Brodda\, Yuu
ki Tadokoro and Kokoro Tanaka (arXiv: 2506.05778\, 2506.08050).\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akio Kawauchi
DTSTART:20250730T073000Z
DTEND:20250730T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/101
DESCRIPTION:Title: A survey on smooth unknotting of a surface-knot in the 4-spa
ce\nby Akio Kawauchi as part of Moscow-Beijing topology seminar\n\n\nA
bstract\nIt is explained how a smooth surface-knot in 4-space with infinit
e cyclic fundamental group is a trivial surface-knot (i.e.\, the boundary
of a smoothly embedded handlebody) in the 4-space. It is also explained ho
w a smooth surface-link in 4-space with meridian-based free fundamental gr
oup is a trivial surface-link (i.e.\, the boundary of smoothly embedded di
sjoint handlebodies) in the 4-space. For these proofs\, the concept of an
orthogonal 2-handle pair on a surface-link is introduced and the propertie
s are explained\, with the property of uniqueness being particularly essen
tial.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianru Duan
DTSTART:20250813T073000Z
DTEND:20250813T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/102
DESCRIPTION:Title: The L^2 Alexander torsion for links and its leading coeffici
ent\nby Jianru Duan as part of Moscow-Beijing topology seminar\n\n\nAb
stract\nThe L^2-Alexander torsion is an invariant associated to a 3-manifo
ld and an 1-cohomology class. For an oriented link\, this invariant is a r
eal function with many properties similar to the classical Alexander polyn
omial. In this talk\, I will first review the basics of L^2-theory of 3-ma
nifolds (e.g. L^2-betti numbers\, L^2-torsions)\, then discuss the "leadin
g coefficient" of the L^2-Alexander torsion and show its connection with G
abai's sutured manifold theory and the guts theory recently developed by A
gol-Zhang.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arunima Ray
DTSTART:20250820T073000Z
DTEND:20250820T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/103
DESCRIPTION:Title: The double star construction\nby Arunima Ray as part of
Moscow-Beijing topology seminar\n\n\nAbstract\nI will describe a new strat
egy to construct a pair of closed\, smooth 4-manifolds\, that are homotopy
equivalent but not homeomorphic\, inspired by the star construction. I wi
ll specifically focus on the constructive step\, which consists of a seque
nce of explicit geometric manoeuvres.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Pan
DTSTART:20250827T083000Z
DTEND:20250827T100000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/104
DESCRIPTION:Title: Augmentations and Exact Lagrangian surfaces\nby Yu Pan a
s part of Moscow-Beijing topology seminar\n\n\nAbstract\nExact Lagrangian
surfaces are important objects in the derived Fukaya category. Augmentatio
ns are objects of the augmentation category\, which is the contact analog
of the Fukaya category. In this talk\, we discuss various relations betwee
n augmentations and exact Lagrangian surfaces. In particular\, we realize
augmentations\, which is an algebraic object\, fully geometrically via exa
ct Lagrangian surfaces.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yannik Schuler
DTSTART:20250806T073000Z
DTEND:20250806T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/105
DESCRIPTION:Title: Refined Gromov-Witten invariants\nby Yannik Schuler as p
art of Moscow-Beijing topology seminar\n\n\nAbstract\nGromov-Witten theory
is a framework for enumerating holomorphic curves in a Kähler manifold X
. The case where X is Calabi-Yau of complex dimension three is particularl
y rich and features connections to seemingly unrelated areas in mathematic
s and mathematical physics\, for instance knot invariants. I will introduc
e a refinement of Gromov-Witten invariants of Calabi-Yau threefolds as pro
posed in joint work with A. Brini. I will explain how our proposal formali
ses certain ideas in mathematical physics and mention several sanity check
s our proposal passes. I will discuss applications and relations between o
ur refinement and other developments in enumerative geometry. Special emph
asis will be on refined knot invariants where I will comment on current ob
structions and possible gains.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eiji Ogasa
DTSTART:20250917T073000Z
DTEND:20250917T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/106
DESCRIPTION:Title: An extension of Khovanov-Lipshitz-Sarkar homotopy type\n
by Eiji Ogasa as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIt
is an open question whether Khovanov-Lipshitz-Sarkar homotopy type can be
extend to all manifolds. Kauffman\, Nikonov\, and the speaker extend it t
o thickened surfaces.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ueki Jun\, Hyuga Yoshizaki
DTSTART:20250924T073000Z
DTEND:20250924T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/107
DESCRIPTION:Title: The p-adic class numbers of number fields\, elliptic curves\
, knots\, and graphs\nby Ueki Jun\, Hyuga Yoshizaki as part of Moscow-
Beijing topology seminar\n\n\nAbstract\npart 1 -- graphs -- (30 min) \n
by Jun Ueki (Ochanomizu University) \n\npart 2 --- number fields\, elli
ptic curves\, and knots -- (60 min) \n by Hyuga Yoshizaki (Tokyo Science
University) \n\nAbstract. \nLet $p$ be a prime number. As initially poi
nted out by Sinnott--Han--Kisilevsky and afterward re-discovered by us\, i
n a pro-$p$ extension of number fields or its various analogues\, the clas
s number p-adically converges. In a topological setting\, the $p$-adic lim
it value (say\, the $p$-adic class number) may be interpreted as Kionke's
$p$-adic torsion. \nWe will give numerical observations on this phenomenon
and point out further interests\, especially in a view of Lang--Trotter c
onjecture. \n(This talk is partially based on joint works with Reo Kobayas
hi and Sohei Tateno.)\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Abrosimov
DTSTART:20250910T073000Z
DTEND:20250910T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/108
DESCRIPTION:Title: Volumes of non-Euclidean tetrahedra\nby Nikolay Abrosimo
v as part of Moscow-Beijing topology seminar\n\n\nAbstract\nThe talk will
provide an overview of the latest results on finding exact formulas for ca
lculating the volumes of hyperbolic tetrahedra. The classical formula of G
. Sforza [1] expresses the volume of a general hyperbolic tetrahedron in t
erms of dihedral angles. Its modern proof is proposed in [2]\, where a ver
sion of the Sforza formula for the volume of a spherical tetrahedron is al
so given. A formula in terms of edge lengths was obtained in [3]. The know
n formulas for the volume of a general hyperbolic tetrahedron are complica
ted and cannot always be applied to calculate the volumes of more complex
polyhedra. A natural question arises about finding simpler formulas for su
fficiently wide families of hyperbolic tetrahedra. \nIn the second part of
the talk\, we will consider hyperbolic tetrahedra of special types: ideal
\, biorthogonal\, trirectangular\, and their generalizations. The volume o
f an ideal and biorthogonal hyperbolic tetrahedron was known to N.I. Lobac
hevsky. We will present new formulas for calculating the volume and normal
ized volume of a hyperbolic trirectangular tetrahedron [4]\, as well as it
s generalization for a 4-parameter family of tetrahedra with one edge orth
ogonal to a face. The latter formulas can be used to calculate the volumes
of more complex polyhedra in Lobachevsky space.\nAt the end of the talk\,
we will present a new formula for calculating the volume of a spherical t
rirectangular tetrahedron [5]. The list of Coxeter's spherical tetrahedra
was constructed in [6]. Coxeter showed that there are 11 types of such tet
rahedra in S^3. We will show that exactly 5 of these types belong to the f
amily of trirectangular tetrahedra. We will calculate their volumes to ver
ify our formula.\n\nReferences:\n[1] Sforza G.\, Spazi metrico-proiettivi.
Ricerche di Estensionimetria Integrale. Ser. 1907. III\, VIII (Appendice)
. P.41–66.\n\n[2] Abrosimov N.V.\, Mednykh A.D.\, Volumes of polytopes i
n constant curvature spaces. Fields Inst. Commun. 2014. V.70. P.1–26. ar
Xiv:1302.4919\n\n[3] Abrosimov N.\, Vuong B.\, Explicit volume formula for
a hyperbolic tetrahedron in terms of edge lengths. Journal of Knot Theory
and Its Ramifications. 2021. V.30. No.10\, 2140007. arXiv:2107.03004\n\n[
4] Abrosimov N.\, Stepanishchev S.\, The volume of a trirectangular hyperb
olic tetrahedron. Siberian Electronic Mathematicsl Reports. 2023. V.20. No
.1\, P.275–284.\n\n[5] Abrosimov N.\, Bayzakova B.\, The volume of a sph
erical trirectangular tetrahedron. Siberian Electronic Mathematicsl Report
s. 2025. V.22. No.1\, P.892–904.\n\n[6] Coxeter H.S.M.\, Discrete groups
generated by reflections. Ann. Math. 1934. V.35. P.588–621.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Taranenko
DTSTART:20250903T073000Z
DTEND:20250903T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/109
DESCRIPTION:Title: Multidimensional matrices in algebraic hypergraph theory
\nby Anna Taranenko as part of Moscow-Beijing topology seminar\n\n\nAbstra
ct\nThe main goal of the presented study is to develop methods for working
with multidimensional matrices that can be applied to problems of existen
ce and enumeration of various structures in hypergraphs. Many results in t
he search for substructures in graphs are based on certain correspondences
between graphs and matrices and the application of linear algebra methods
. Among the most important topics in the combinatorial matrix theory are t
he representation of graphs using adjacency and incidence matrices\, the K
onig-Hall theorem for systems of distinct representatives\, the permanents
of doubly stochastic matrices\, and Latin squares. We generalize these di
rections to multidimensional matrices and hypergraphs and lay the foundati
ons of the combinatorial theory of multidimensional matrices.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Tiskin
DTSTART:20251008T073000Z
DTEND:20251008T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/110
DESCRIPTION:Title: The surprising algebra of string comparison\nby Alexande
r Tiskin as part of Moscow-Beijing topology seminar\n\n\nAbstract\nThere i
s a surprising close connection between three seemingly unrelated structur
es:\n\n- the longest common subsequence of strings and its behavior under
string concatenation\;\n- a certain class of integer matrices (unit-Monge
matrices)\, considered as a monoid under tropical multiplication\;\n- the
Hecke monoid\, or "sticky braid" monoid\, which can be regarded as the cla
ssical braid group where inversion is replaced by idempotence of the gener
ators.\n\nThese structures\, despite their different nature\, are in fact
isomorphic\, so they represent different views of the same underlying stru
cture. We will describe an efficient multiplication algorithm in this stru
cture and its applications to various string comparison and approximate pa
ttern matching problems.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shoma Sugimoto
DTSTART:20251001T073000Z
DTEND:20251001T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/111
DESCRIPTION:Title: An abelian categorification of $\\hat{Z}$-invariants\nby
Shoma Sugimoto as part of Moscow-Beijing topology seminar\n\n\nAbstract\n
The $\\hat{Z}$-invariant is a $q$-series valued quantum invariant for (neg
ative definite plumbed) 3-manifolds introduced by Gukov--Pei--Putrov--Vafa
in 2017. It provides not only a $q$-expansion of the Witten--Reshetikhin-
-Turaev invariant\, but also rich examples of ``spoiled" modular forms suc
h as mock/false theta functions. The latter fact suggests the existence of
non-rational vertex operator algebras (log VOAs) with $\\hat{Z}$-invarian
ts as their $q$-characters. However\, the study of log VOAs is still under
developed\, and no examples of such log VOAs have been found so far except
for the two easiest cases (3- or 4-leg star graphs).\nThis talk will outl
ine the ``nested Feigin--Tipunin construction" introduced and developed by
the speaker to provide a unified construction/research methodology of the
above correspondence between log VOAs and (negative definite plumbed) 3-m
anifolds. It enables us to construct and study the abelian category of mod
ules over the hypothetical log VOAs via the recursive application of the p
urely Lie algebraic geometric representation theory of FT construction. In
particular\, the corresponding $\\hat{Z}$-invariants are reconstructed in
the Grothendieck group via the recursive application of the Weyl-type cha
racter formula. From a theoretical physics perspective\, the nested FT con
struction can be viewed as the algebraic counterpart to the contribution f
rom 3d $\\mathcal{N}=2$ theory in the $\\hat{Z}$-invariants.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Dzhamay
DTSTART:20251022T073000Z
DTEND:20251022T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/112
DESCRIPTION:Title: On a positivity property of a solution of discrete Painlevé
equations\nby Anton Dzhamay as part of Moscow-Beijing topology semina
r\n\n\nAbstract\nWe consider a particular example of a discrete Painlevé
equation arising from a construction of quantum minimal surfaces by Arnlin
d\, Hoppe and Kontsevich. Observing that this equation corresponds to a ve
ry special choice of parameters (root variables) in the Space of Initial C
onditions for the differential Painlevé V equation\, we show that some ex
plicit special function solutions\, written in terms of modified Bessel fu
nctions\, for d-PV yield the unique positive solution for some initial val
ue problem for the discrete Painlevé eqyuation needed for quantum minimal
surfaces. This is a joint work with Peter Clarkson\, Andy Hone\, and Ben
Mitchell.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangzhou Liu
DTSTART:20251015T073000Z
DTEND:20251015T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/113
DESCRIPTION:Title: On the Unfaithfulness of the Manturov-Nikonov Map\nby Ya
ngzhou Liu as part of Moscow-Beijing topology seminar\n\n\nAbstract\nThe r
epresentation theory of braid groups has advanced significantly beyond tha
t of classical knots\, with several foundational linear representations es
tablished. These include the Burau representation (which is known to be un
faithful for Bn when n≥5)\, the Temperley–Lieb representation (closely
related to the Jones polynomial)\, and the Lawrence–Krammer–Bigelow r
epresentation (faithful for all n≥1). In 2022\, Professor Manturov and P
rofessor Nikonov introduced a map from classical braids to virtual braids\
, extending the framework of braid group representations into the domain o
f virtual knot theory. This talk will demonstrate that the Manturov-Nikono
v map is unfaithful by constructing explicit counterexamples.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Kalinin
DTSTART:20251105T073000Z
DTEND:20251105T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/114
DESCRIPTION:Title: Tropical Weil Reciprocity\nby Nikita Kalinin as part of
Moscow-Beijing topology seminar\n\n\nAbstract\nThe classical Weil reciproc
ity law is a fundamental result in the theory of algebraic curves\, statin
g that for two meromorphic functions on a compact Riemann surface\, the pr
oduct of the values of one function at the divisors of the other is equal
to the reciprocal product. In this talk\, we explore a tropical analogue o
f this law.\n \n We will begin by introducing tropical curves and tropic
al meromorphic functions. We then state and prove the tropical Weil recipr
ocity law\, which takes a strikingly simple linear form. This tropical per
spective not only provides a new\, combinatorial viewpoint but also leads
to an elegant proof of the original\, classical Weil reciprocity law. The
proof strategy involves decomposing the Riemann surface into simple pieces
(cylinders) and observing how the relevant contributions cancel upon glui
ng.\n \n Finally\, we will discuss how this framework allows for the con
struction of a tropical Weil pairing on the group of divisors of degree ze
ro\, drawing an analogy with electrical networks and suggesting a connecti
on to its classical counterpart. This is joint work with M. Magin.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toshio Saito
DTSTART:20251119T073000Z
DTEND:20251119T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/115
DESCRIPTION:Title: From Flow Spines to Virtual Knot Diagrams: A Risandle Approa
ch to 3-Manifold Invariants\nby Toshio Saito as part of Moscow-Beijing
topology seminar\n\n\nAbstract\nEvery oriented closed 3-manifold admits a
flow spine\, that is\, a spine in a “good” position with respect to a
given nonsingular flow. A flow spine can be represented by a virtual knot
diagram\, where equivalence is defined through a family of local moves di
fferent from the classical Reidemeister moves.\nIn this talk\, we introduc
e a modified version of the quandle algebra\, originally useful in knot th
eory\, to define a new notion of “coloring” for closed 3-manifolds. Th
is coloring yields a topological invariant of 3-manifolds. Furthermore\, I
will explain how this invariant is related to the fundamental group of th
e manifold. The correspondence between colorings and group representations
will be illustrated concretely using the Poincaré homology sphere as an
example. This work is a joint project with Ippei Ishii and Takuji Nakamura
.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20251029T073000Z
DTEND:20251029T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/116
DESCRIPTION:Title: A characterization of virtual knots as knots in $S_{g} \\tim
es S^{1}$\nby Seongjeong Kim as part of Moscow-Beijing topology semina
r\n\n\nAbstract\nIn this talk we will show that virtual knots are embedded
in the set of knots in $S_{g} \\times S^{1}$. We will also provide a suff
icient condition for knots in $S_{g} \\times S^{1}$ to have virtual knot d
iagrams.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Bazhenov (Sobolev Institute of Mathematics\, Novosibirsk\,
Russia)
DTSTART:20251203T073000Z
DTEND:20251203T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/117
DESCRIPTION:Title: On computability-theoretic aspects of Stone spaces\nby N
ikolay Bazhenov (Sobolev Institute of Mathematics\, Novosibirsk\, Russia)
as part of Moscow-Beijing topology seminar\n\n\nAbstract\nThe roots of com
putable analysis go back to the seminal work of Turing (1936). One of the
main directions in contemporary computable analysis studies computability
aspects of Polish spaces. A computable Polish space is a Polish space equi
pped with a distinguished dense countable sequence of points such that the
distances between these points are uniformly computable.\nIn the talk\, w
e focus on Stone spaces. Recall that a Stone space is a compact and totall
y disconnected Hausdorff space. The classical result of Stone established
a duality between the category of Stone spaces and the category of Boolean
algebras. We give an overview of some recent results on the computability
-theoretic properties of separable Stone spaces. In particular\, we discus
s effective versions of the Stone duality.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaebaek Lee
DTSTART:20251112T073000Z
DTEND:20251112T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/118
DESCRIPTION:Title: The Ramsey Multiplicity Problem\nby Jaebaek Lee as part
of Moscow-Beijing topology seminar\n\n\nAbstract\nA graph $H$ is said to b
e \\emph{common} if the number of monochromatic copies of $H$ is asymptoti
cally minimized by a random colouring. It is well known that the disjoint
union of two common graphs may be uncommon\; e.g.\, $K_2$ and $K_3$ are co
mmon\, but their disjoint union is not. We investigate the commonality of
disjoint unions of multiple copies of $K_3$ and $K_2$. As a consequence of
our results\, we obtain the first example of a pair of uncommon graphs wh
ose disjoint union is common. Our approach is to reduce the problem of sho
wing that certain disconnected graphs are common to a constrained optimiza
tion problem in which the constraints are derived from supersaturation bou
nds related to Razborov's Triangle Density Theorem. We also improve the bo
unds on the Ramsey multiplicity constant of a triangle with a pendant edge
and the disjoint union of $K_3$ and $K_2$.\nFox and Wigderson recently id
entified a large family of graphs whose Ramsey multiplicity constants are
attained by sequences of ``Tur\\'an colourings\;'' i.e. colourings in whic
h one of the colour classes forms the edge set of a balanced complete mult
ipartite graph. Each graph in their family comes from taking a connected n
on-3-colourable graph with a critical edge and adding many pendant edges.
\nWe focus on finding smaller graphs whose Ramsey multiplicity constants a
re achieved by Tur\\'an colourings. While Fox and Wigderson provide many
examples\, their smallest constructions involve graphs with at least $10^{
66}$ vertices. In contrast\, we identify a graph on only $10$ vertices who
se Ramsey multiplicity constant is achieved by Tur\\'an colourings. To pro
ve this\, we apply the method developed earlier and use a powerful techniq
ue known as the flag algebra method\, assisted by semi-definite programmin
g.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jun Wang
DTSTART:20251210T073000Z
DTEND:20251210T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/119
DESCRIPTION:Title: The multiple points of maps from sphere to Euclidean space\nby Jun Wang as part of Moscow-Beijing topology seminar\n\n\nAbstract\n
It is obtained some sufficient conditions to guarantee the existence of mu
ltiple points of maps from $S^m$ to $\\mathbb{R}^d$. Our main tool is the
ideal-valued index of $G$-space defined by E. Fadell and S. Husseini. We
obtain more detailed relative positional relationship of multiple points
. It is proved that for a continuous real value function $f: S^m\\rightar
row \\mathbb{R}$ such that $f(-p)=-f(p)$\, if $m+1$ is a power of $2$\,
then there are $m+1$ points $p_1\, \\ldots\, p_{m+1}$ in $S^m$ such that
$f(p_1)=\\cdots=f(p_{m+1})$\, where $p_1\, \\ldots\, p_{m+1}$ are linearl
y dependent and any $m$ points of $p_1\, \\ldots\, p_{m+1}$ are linearly
independent. As a generalization of Hopf's theorem\, we also prove that f
or any continuous map $f: S^m\\rightarrow \\mathbb{R}^d$\, if $m> d$\, the
n there exists a pair of mutually orthogonal points having the same image
in addition to the antipodal points.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Zhang
DTSTART:20251126T073000Z
DTEND:20251126T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/120
DESCRIPTION:Title: Skein lasagna modules and Rozansky-Willis homology\nby M
elissa Zhang as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIn
this talk I will describe joint work with Ian Sullivan\, where we use prop
erties of categorified projectors to prove that the Khovanov skein lasagna
module of $S^2 \\times S^2$ is trivial. Along the way\, we will discover
a relationship between the skein lasagna module of $S^2 \\times D^2$ with
a link $L$ in the boundary and the Rozansky-Willis homology of $L$ inside
$S^2 \\times S^1$. This isomorphism is used in recent joint work with Qiuy
u Ren\, Ian Sullivan\, Paul Wedrich\, and Michael Willis\, where we define
a new version of $gl_2$ skein lasagna modules with 1-dimensional inputs.\
n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Николай Ероховец
DTSTART:20251217T073000Z
DTEND:20251217T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/121
DESCRIPTION:Title: Гиперболические зацепления\, отв
ечающие эйлеровым циклам на идеальных п
рямоугольных гиперболических многогра
нниках\,\nby Николай Ероховец as part of Moscow-B
eijing topology seminar\n\n\nAbstract\nМы расскажем о конс
трукции\, позволяющей по эйлерову циклу C
без трансверсальных самопересечений на
трёхмерном идеальном прямоугольном гип
ерболическом многограннике P построить
зацепление со следующими свойствами: \n(1)
число его компонент равно числу идеальн
ых вершин\, \n(2) дополнение гомеоморфно по
лному гиперболическому многообразию\, с
клеенному из 4-х копий многогранника P и п
олучается из него конструкцией А.Ю.Весни
на-А.Д.Медных\, отвечающей шахматной раск
раске. \n(3) многообразие\, которое двулист
но разветвлённо накрывает сферу вдоль э
того зацепления\, получается конструкци
ей А.Д.Медных для гамильтонова цикла на д
ругом простом многограннике Q\, определя
емым циклом C (зацепления\, получаемые в э
той конструкции были недавно подробно и
сследованы В.Горчаковым). \n\nМы покажем\,
что на каждом идеальном многограннике\,
кроме антипризм\, существует по крайней
мере 7 таких циклов\, а на антипризмах — п
о крайней мере два. При этом на каждой ан
типризме есть один выделенный цикл\, для
которого конструкция сводится к констру
кции У.П.Тёрстона.\n\nКак следствие мы пок
ажем\, что для каждого гамильтонова цикл
а \nна трёхмерном компактном прямоугольн
ом гиперболическом многограннике допол
нение до зацепления из конструкции А.Д.М
едных\, разбивается на 4 идеальных гиперб
олических многогранника (при этом двули
стная накрывающая тоже имеет гиперболич
ескую структуру).\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brett Parker
DTSTART:20260107T073000Z
DTEND:20260107T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/122
DESCRIPTION:Title: Tropical perspectives on Skein modules.\nby Brett Parker
as part of Moscow-Beijing topology seminar\n\n\nAbstract\nI will explain
the connection between tropical curves\, skein modules\, and holomorphic c
urves in log Calabi—Yau 3-folds. In particular\, I will explain a quantu
m deformation of Mikhalkin’s tropical correspondence formula\, and how a
quantum torus lie algebra arises when counting closed holomorphic curves
in some log Calabi—Yau 3-folds. Apart from some pesky factors of i\, thi
s quantum torus lie algebra agrees with the elliptic Hall algebra describi
ng the skein algebra of the thickened torus. In fact\, there is a beautif
ul explicit connection using Ekholm and Shende’s `skeins on branes’ fo
rmalism for counting holomorphic curves with boundaries on Lagrangian bran
es. I will illustrate this through two simple examples\, and explain why t
hose pesky factors of i make me think that the worldsheet skein module int
roduced by Ekholm\, Longhi\, and Nakamura needs a simple modification to a
ccount for some non-local contributions to orientations. The second half
of this talk is work in progress.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rajat Mishra
DTSTART:20251224T073000Z
DTEND:20251224T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/123
DESCRIPTION:Title: Jet Spaces\, Differential Characters\, and Manin Kernels
\nby Rajat Mishra as part of Moscow-Beijing topology seminar\n\n\nAbstract
\nLet K be a field of characteristic zero with a derivation ∂ on it (for
example\, (C(t)\, ∂/∂t)) and G be a smooth commutative group scheme o
ver it. In this talk\, we study the kernel of the differential characters
K(G) of the jet space of G\, known as the Manin kernel of G. When G is an
abelian variety\, Buium showed—using the theory of universal extensions
—that the Manin kernel is a D-group scheme and a finite vectorial extens
ion of G. We extend this result to arbitrary smooth commutative group sche
mes\, proving that the Manin kernel K(G) remains a finite vectorial extens
ion of G. Our approach relies entirely on a detailed understanding of the
structure of jet spaces and also yields a classification of the module of
differential characters in terms of primitive characters\, viewed as a K{
∂}-module. This is joint work with Arnab Saha.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malik Maricar
DTSTART:20251231T073000Z
DTEND:20251231T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/124
DESCRIPTION:Title: Introduction to phenomenological physics theory\, deriving t
he Bohr Volume forms\, current applications in academia and industry\; reg
arding medicine and engineering\nby Malik Maricar as part of Moscow-Be
ijing topology seminar\n\n\nAbstract\nMy goal for the talk is to define th
e Bohr Manifold—from how it came about to deriving its volume forms—Eu
clidean and the other Leibnizian. Thus\, make connections to published lit
erature results including de Sitter by conformal field (4\,5) theory due t
o Juan Maldacena and at least another Juven C. Wang mentioned. Briefly\, d
iscuss progression to the YM-Mass Gap solution and other problems listed b
y the Clay Mathematics Institute. Highlight\, current research work applyi
ng from Manturov\, Nikonov\, Vogan to engineering in medicine and among ot
hers\, Strominger\, Hong Liu\, Harlow\, and Wen Xiao Gang to further physi
cs understanding of our universe invariant of scale\, including mathematic
s made possible by Zhang Wei\, Yun Zhi Wei and many others. Since\, this w
ill be my first ever talk—it will be informational\, remembering the con
ferences and giving thanks to so many speakers presenting their works over
the years contributing to my own research—with the main goal of derivin
g the Bohr Volume Forms and to introduce a promising framework for mathema
ticians. For the talk\, slides will be provided and if available technolog
y permits\, instruction will be on chalkboard.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreani Petrou
DTSTART:20260121T073000Z
DTEND:20260121T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/125
DESCRIPTION:Title: HOMFLY-PT and Kauffman polynomials: for which knots are the
y related?\nby Andreani Petrou as part of Moscow-Beijing topology semi
nar\n\n\nAbstract\nTorus knots are long known to satisfy a special relatio
n between their HOMFLY-PT and Kauffman polynomials\, which has a peculiar
implication in the context of Topological Strings. In this talk\, I will d
escribe infinite families of hyperbolic knots and links that enjoy the sam
e property. These were found via a physics-inspired tool called the Harer-
Zagier (HZ) transform\, which is a version of the Laplace transform that
maps the HOMFLY-PT polynomial into a rational function. It is conjectured
that whenever the latter is factorisable\, the HOMFLY-PT-Kauffman relation
occurs. I will explain how some steps towards a proof of this conjecture
can be made\, at least for 3-strand braids\, by expanding these two-variab
le link polynomials in terms of characters.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andronick Arutyunov
DTSTART:20260128T073000Z
DTEND:20260128T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/126
DESCRIPTION:Title: А combinatorial approach to derivations in algebras.\nb
y Andronick Arutyunov as part of Moscow-Beijing topology seminar\n\n\nAbst
ract\nUsing the following construction\, derivations in the sense of Leibn
iz\, as well as Fox derivatives and some other operators in algebras\, can
be studied. First\, a category (usually a groupoid) is constructed\, and
then the operators are identified with the characters of the category. The
se characters are already can be studied using algebraic and combinatorial
methods\, which leads to questions related to rough geometry.\n\nThis app
roach\, which was presented in a series of papers by the author and Profes
sor Mishchenko\, will be discussed.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia V. Maslova (N.N. Krasovskii Institute of Mathematics and M
echanics UB RAS\, Yekaterinburg\, Russia Ural Mathematical Center\, Yekate
rinburg\, Russia S.L. Sobolev Institute of Mathematics SB RAS\, Novosibirs
k\, Russia)
DTSTART:20260114T073000Z
DTEND:20260114T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/127
DESCRIPTION:Title: On Gruenberg-Kegel graphs and beyond\nby Natalia V. Masl
ova (N.N. Krasovskii Institute of Mathematics and Mechanics UB RAS\, Yekat
erinburg\, Russia Ural Mathematical Center\, Yekaterinburg\, Russia S.L. S
obolev Institute of Mathematics SB RAS\, Novosibirsk\, Russia) as part of
Moscow-Beijing topology seminar\n\n\nAbstract\nThe Gruenberg--Kegel graph
(or the prime graph) of a finite group $G$ is a simple graph whose vertice
s are the prime divisors of $|G|$\, with primes $p$ and $q$ adjacent in th
is graph if and only if $pq$ is an element order of $G$. The concept of Gr
uenberg--Kegel graph proved to be very useful in finite group theory and i
n algebraic combinatorics as well as with connection to research of some c
ohomological questions in integral group rings. In this talk\, we discuss
recent results on characterization of finite groups by Gruenberg-Kegel gra
ph and by isomorphism type of Gruenberg-Kegel graph as well as combinatori
al properties of Gruenberg--Kegel graphs.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Ekholm
DTSTART:20260211T073000Z
DTEND:20260211T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/128
DESCRIPTION:Title: Skein valued curve counting\nby Tobias Ekholm as part of
Moscow-Beijing topology seminar\n\n\nAbstract\nWe describe how counting c
urves in a symplectic Calabi-Yau 3-fold with boundary in a Maslov zero Lag
rangian give a deformation invariant curve count. We then survey applicati
ons including a proof of the Ooguri-Vafa conjecture and various skein rec
ursion relations.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Butian Zhang
DTSTART:20260204T073000Z
DTEND:20260204T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/129
DESCRIPTION:Title: Combinatorial 1-cocycles in the space of long knots\nby
Butian Zhang as part of Moscow-Beijing topology seminar\n\n\nAbstract\nThe
space of long knots (i.e.\, the smooth embeddings of ℝ into ℝ³ that
agree with the standard embedding of the x-axis outside the interval [-1\,
1]) has been studied from various perspectives. In this talk\, we adopt a
combinatorial approach to loops and 1-cocycles in this space. Using Gauss
diagrams\, we construct two nontrivial linearly independent combinatorial
1-cocycles of order 4 over ℤ and an additional one over ℤ/2ℤ. We al
so calculate their values on several arcs and loops in the space of long k
nots. Furthermore\, we will discuss the joint work with T. Fiedler on the
quantum equations derived from a regular 1-cocycle based on the HOMFLY-PT
polynomial.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiquan Ren (School of Mathematics and Statistics\, Henan Universi
ty\, China)
DTSTART:20260225T073000Z
DTEND:20260225T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/130
DESCRIPTION:Title: Homological obstructions for regular embeddings of graphs\nby Shiquan Ren (School of Mathematics and Statistics\, Henan University
\, China) as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIn thi
s talk\, we develop the hypergraph obstruction for the existence of k-regu
lar embeddings concretely and give some homological obstructions for the k
-regular embeddings of graphs by\nusing the embedded homology of sub-hyper
graphs of the (k−1)-skeleton of the independence\ncomplexes. We regard r
egular embeddings of graphs equivalently as geometric realizations of the
independence complexes and consequently regard them equivalently as simpli
cial\nembeddings of the independence complexes into the vectorial matroids
. We prove that if\nthere exists a k-regular embedding of a graph\, then t
here is an induced homomorphism from\nthe embedded homology of the sub-hyp
er(di)graphs of the (k − 1)-skeleton of the (directed)\nindependence com
plexes to the homology of (directed) matroids. Moreover\, if there exists\
ncertain triple of graphs where each graph has a k-regular embedding\, the
n there are induced commutative diagrams of certain Mayer-Vietoris sequenc
es of the embedded homology\nof hyper(di)graphs\, the homology of (directe
d) independence complexes and the homology\nof matroids. Furthermore\, if
there exists certain couple of graphs where each graph has\na k-regular em
bedding\, then there are induced commutative diagrams of certain Kunneth\n
type short exact sequences of the embedded homology of hyper(di)graphs\, t
he homology of\n(directed) independence complexes and the homology of matr
oids.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Feidler Thomas
DTSTART:20260218T073000Z
DTEND:20260218T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/131
DESCRIPTION:Title: Polynomial 1-cocycles for closed braids and tangle equations
for knots\nby Feidler Thomas as part of Moscow-Beijing topology semin
ar\n\n\nAbstract\nWe construct a combinatorial 1-cocycle for closed braids
. When applied to the full rotation of the solid torus around its core it
gives a Laurent polynomial which can sometimes detect the non-invertibilit
y of the closed braid (what quantum invariants fail to do). In the case of
knots in 3-space we use another type of 1-cocycles to introduce the tangl
e equations. If they have no solution\, then the knots are not isotopic. O
n the other hand\, each solution gives quantitative information about any
isotopy which relates the two knots.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaiane Panina
DTSTART:20260401T073000Z
DTEND:20260401T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/132
DESCRIPTION:Title: A new proof of the Milnor – Wood theorem\, and beyond\
nby Gaiane Panina as part of Moscow-Beijing topology seminar\n\n\nAbstract
\nThe Milnor--Wood inequality states that if a (topological) oriented circ
le bundle over an orientable surface of genus $g$\nhas a smooth transverse
foliation\, then the Euler class of the bundle satisfies $|E|\\leq 2g-2$.
\nWe give a new proof of the inequality based on a (previously proven by t
he authors) local formula which computes \n$E$\n from the singularities of
a quasisection and present some more applications of this approach.\n(Bas
ed on joint works with Ilya Alekseev\, Ivan Nasonov\, Timur Shamazov and
Maksim Turevskii)\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George B. Shabat
DTSTART:20260304T073000Z
DTEND:20260304T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/133
DESCRIPTION:Title: Introduction to dessins d'enfants Theory\nby George B. S
habat as part of Moscow-Beijing topology seminar\n\n\nAbstract\nThe theory
of dessins d'enfants was created by Alexander Grothendieck from 1972 to 1
984. After a short historical overview I plan to talk about this theory in
terms of the three-language vocabluary\, relating two-dimension topology\
, group theory and algebraic geometry. The simplest examples will be provi
ded.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semih Ozlem
DTSTART:20260318T073000Z
DTEND:20260318T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/134
DESCRIPTION:Title: Parity in Tensor Categories: From Hexagon Counting to Virtua
l Knots\nby Semih Ozlem as part of Moscow-Beijing topology seminar\n\n
\nAbstract\nTensor categories come equipped with associativity constraints
\nϕ:(X⊗Y)⊗Z≅X⊗(Y⊗Z)\nand commutativity constraints\nΨ:X⊗Y≅
Y⊗X\,\nwhich must satisfy compatibility conditions encoded in hexagon di
agrams. For fixed objects X\,Y\,Z\, the full diagram of all tensor product
s contains 20 distinct hexagons. A careful counting reveals 8 hexagons tha
t obey an alternation rule (edges alternate between associativity and comm
utativity) and 12 that do not. Under the natural S_3 action permuting X\,Y
\,Z\, these hexagons fall into orbits whose sizes (6 and 2 for alternating
hexagons) point to a mod 2 structure.\n \nWe show that this mod 2 structu
re can be interpreted as a parity grading on commutativity isomorphisms\,
satisfying a cocycle condition\np(X\,Y)+p(X⊗Y\,Z)≡p(Y\,Z)+p(X\,Y⊗Z)m
od2.\nThis parity function defines a parity projection functor Π:C→C_vi
rtual that sends even-parity commutativity isomorphisms to identities whil
e preserving odd-parity ones.\n \nThis functor provides a categorical real
ization of Manturov's map from the classical world to the virtual world in
knot theory. When applied to the braided tensor category of virtual tangl
es\, the construction recovers the parity bracket invariant. The two orbit
s of alternating hexagons correspond to the two cohomology classes in H2(S
3\,Z2)≅Z2\, revealing a deep connection between tensor categories\, knot
parity\, and group cohomology.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiangui Zhao
DTSTART:20260311T073000Z
DTEND:20260311T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/135
DESCRIPTION:Title: Growth of associated monomial algebras and Manturov groups\nby Xiangui Zhao as part of Moscow-Beijing topology seminar\n\n\nAbstra
ct\nIt is well-known that an associative algebra shares the same growth an
d Gelfand-Kirillov dimension (GK-dimension) as its associated monomial alg
ebra with respect to a degree-lexicographic order. In this talk\, we discu
ss the relationship between the GK-dimension of an associative algebra and
that of its associated monomial algebra with respect to a monomial order.
As an application\, we study the growth of Manturov groups\, which were i
ntroduced by V. Manturov in 2015.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Shabat
DTSTART:20260325T073000Z
DTEND:20260325T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/136
DESCRIPTION:Title: Introduction to dessins d'enfants(continued)\nby George
Shabat as part of Moscow-Beijing topology seminar\n\n\nAbstract\nThe 3-lan
guage dictionary will be presented\, relating certain objects in\n1) Bi-
dimensional topology\;\n2) Group theory\;\n3) Arithmetic geometry.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kursat Sozer
DTSTART:20260408T073000Z
DTEND:20260408T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/137
DESCRIPTION:Title: Kuperberg-type invariants of maps from 3-manifolds to homoto
py 2-types\nby Kursat Sozer as part of Moscow-Beijing topology seminar
\n\n\nAbstract\nTopological quantum field theories (TQFTs) provide a power
ful framework for constructing invariants of manifolds. A natural extensio
n is given by homotopy quantum field theories (HQFTs)\, where manifolds ar
e equipped with maps to a fixed target space\, refining invariants to depe
nd on homotopy classes of maps. In this talk\, I begin by recalling Dijkgr
aaf–Witten invariants and their state-sum description\, and explain how
they extend to HQFTs with target BG. I then discuss the passage from group
s to crossed modules\, which serve as algebraic models for homotopy 2-type
s. Next\, I describe the algebraic structures underlying HQFTs with 2-type
targets\, focusing on crossed modules and their tensor-categorical and Ho
pf-algebraic counterparts. In particular\, I explain how Hopf crossed modu
le coalgebras arise naturally and how they relate to graded fusion-type st
ructures. Finally\, I present joint work with Alexis Virelizier\, where we
construct Kuperberg-type invariants for pairs (M\,g)\, with g \\in\n [M\
,B\\chi]\n\, where B\\chi is the classifying space of a crossed module \\c
hi. The construction uses \\chi-labeled Heegaard diagrams together with in
volutory Hopf \\chi-coalgebras. The resulting invariant extends the classi
cal Kuperberg invariant and admits a natural interpretation in terms of fl
at principal 2-bundles over closed oriented 3-manifolds.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Zheglov
DTSTART:20260429T073000Z
DTEND:20260429T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/138
DESCRIPTION:by Alexander Zheglov as part of Moscow-Beijing topology semina
r\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Shabat
DTSTART:20260415T073000Z
DTEND:20260415T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/139
DESCRIPTION:Title: Introduction to dessins d'enfants(continued)\nby George
Shabat as part of Moscow-Beijing topology seminar\n\n\nAbstract\nThe categ
ory of dessins d'enfants is equivalent to the category of Belyi pairs. The
problem of constructive realization of this equivalence will be discussed
and some examples presented.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xu Binbin
DTSTART:20260506T073000Z
DTEND:20260506T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/140
DESCRIPTION:by Xu Binbin as part of Moscow-Beijing topology seminar\n\nAbs
tract: TBA\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20260422T073000Z
DTEND:20260422T090000Z
DTSTAMP:20260422T225921Z
UID:Mos-Bei-top-seminar/141
DESCRIPTION:Title: $G_{n}^{3}$ group and graph-valued invariant\nby Seongje
ong Kim as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIn this
talk we will introduce one modification of $G_{n}^{3}$ group and construct
a map from the braid group to frame 6-valent *-graph with leaves construc
ted by using $G_{n}^{3}$. By extending this idea we construct a knot invar
iant valued in equivalence class of graphs up to local moves by using plat
closure of braids.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/141/
END:VEVENT
END:VCALENDAR