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CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:Michael Shapiro
DTSTART;VALUE=DATE-TIME:20230712T073000Z
DTEND;VALUE=DATE-TIME:20230712T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20230719T073000Z
DTEND;VALUE=DATE-TIME:20230719T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20230802T073000Z
DTEND;VALUE=DATE-TIME:20230802T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20230809T073000Z
DTEND;VALUE=DATE-TIME:20230809T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20230726T073000Z
DTEND;VALUE=DATE-TIME:20230726T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20230816T073000Z
DTEND;VALUE=DATE-TIME:20230816T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20230823T073000Z
DTEND;VALUE=DATE-TIME:20230823T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20230830T073000Z
DTEND;VALUE=DATE-TIME:20230830T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20230906T073000Z
DTEND;VALUE=DATE-TIME:20230906T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20230927T073000Z
DTEND;VALUE=DATE-TIME:20230927T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20230913T073000Z
DTEND;VALUE=DATE-TIME:20230913T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20230920T073000Z
DTEND;VALUE=DATE-TIME:20230920T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20231004T073000Z
DTEND;VALUE=DATE-TIME:20231004T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20231025T073000Z
DTEND;VALUE=DATE-TIME:20231025T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20231011T073000Z
DTEND;VALUE=DATE-TIME:20231011T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20231115T073000Z
DTEND;VALUE=DATE-TIME:20231115T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20231122T053000Z
DTEND;VALUE=DATE-TIME:20231122T070000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20231206T073000Z
DTEND;VALUE=DATE-TIME:20231206T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20231213T073000Z
DTEND;VALUE=DATE-TIME:20231213T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20231220T073000Z
DTEND;VALUE=DATE-TIME:20231220T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240103T073000Z
DTEND;VALUE=DATE-TIME:20240103T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20231227T073000Z
DTEND;VALUE=DATE-TIME:20231227T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240110T073000Z
DTEND;VALUE=DATE-TIME:20240110T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240117T073000Z
DTEND;VALUE=DATE-TIME:20240117T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240124T073000Z
DTEND;VALUE=DATE-TIME:20240124T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240131T073000Z
DTEND;VALUE=DATE-TIME:20240131T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240207T073000Z
DTEND;VALUE=DATE-TIME:20240207T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240221T073000Z
DTEND;VALUE=DATE-TIME:20240221T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240228T073000Z
DTEND;VALUE=DATE-TIME:20240228T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240320T073000Z
DTEND;VALUE=DATE-TIME:20240320T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240306T073000Z
DTEND;VALUE=DATE-TIME:20240306T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240403T073000Z
DTEND;VALUE=DATE-TIME:20240403T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240313T073000Z
DTEND;VALUE=DATE-TIME:20240313T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240410T073000Z
DTEND;VALUE=DATE-TIME:20240410T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240327T073000Z
DTEND;VALUE=DATE-TIME:20240327T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240515T073000Z
DTEND;VALUE=DATE-TIME:20240515T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240417T073000Z
DTEND;VALUE=DATE-TIME:20240417T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240424T073000Z
DTEND;VALUE=DATE-TIME:20240424T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240522T073000Z
DTEND;VALUE=DATE-TIME:20240522T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240501T073000Z
DTEND;VALUE=DATE-TIME:20240501T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240731T073000Z
DTEND;VALUE=DATE-TIME:20240731T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240508T073000Z
DTEND;VALUE=DATE-TIME:20240508T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240529T073000Z
DTEND;VALUE=DATE-TIME:20240529T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240612T073000Z
DTEND;VALUE=DATE-TIME:20240612T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240626T073000Z
DTEND;VALUE=DATE-TIME:20240626T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240605T073000Z
DTEND;VALUE=DATE-TIME:20240605T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240814T073000Z
DTEND;VALUE=DATE-TIME:20240814T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240619T073000Z
DTEND;VALUE=DATE-TIME:20240619T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240703T073000Z
DTEND;VALUE=DATE-TIME:20240703T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240710T073000Z
DTEND;VALUE=DATE-TIME:20240710T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240828T073000Z
DTEND;VALUE=DATE-TIME:20240828T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240821T073000Z
DTEND;VALUE=DATE-TIME:20240821T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240807T073000Z
DTEND;VALUE=DATE-TIME:20240807T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240911T073000Z
DTEND;VALUE=DATE-TIME:20240911T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20241009T073000Z
DTEND;VALUE=DATE-TIME:20241009T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240904T073000Z
DTEND;VALUE=DATE-TIME:20240904T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20241002T073000Z
DTEND;VALUE=DATE-TIME:20241002T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240918T073000Z
DTEND;VALUE=DATE-TIME:20240918T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20240925T073000Z
DTEND;VALUE=DATE-TIME:20240925T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20241016T073000Z
DTEND;VALUE=DATE-TIME:20241016T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
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;VALUE=DATE-TIME:20241023T073000Z
DTEND;VALUE=DATE-TIME:20241023T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
UID:Mos-Bei-top-seminar/64
DESCRIPTION:by Andrey Y. Vesnin as part of Moscow-Beijing topology seminar
\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hayato Imori
DTSTART;VALUE=DATE-TIME:20241030T073000Z
DTEND;VALUE=DATE-TIME:20241030T090000Z
DTSTAMP;VALUE=DATE-TIME:20241016T065916Z
UID:Mos-Bei-top-seminar/65
DESCRIPTION:by Hayato Imori as part of Moscow-Beijing topology seminar\n\n
Abstract: TBA\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/65/
END:VEVENT
END:VCALENDAR