BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Ruochuan Liu (Peking University)
DTSTART;VALUE=DATE-TIME:20201023T101500Z
DTEND;VALUE=DATE-TIME:20201023T111500Z
DTSTAMP;VALUE=DATE-TIME:20210124T161434Z
UID:BeijingMoscowColloquium/1
DESCRIPTION:Title: Topological cyclic homology for p-adic local fields\nby
Ruochuan Liu (Peking University) as part of Beijing Moscow Mathematics Co
lloquium\n\n\nAbstract\nWe introduce a new approach to compute topological
cyclic homology using the descent spectral sequence and the algebraic Tat
e spectral sequence. We carry out computations in the case of a $p$-adic l
ocal field with coefficient ${\\mathbb F}_p$. Joint work with Guozhen Wang
.\n\nMeeting ID: 648 6454 8936 Password: 899678\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Frolenkov (Steklov Mathematical Institute of RAS)
DTSTART;VALUE=DATE-TIME:20201023T111500Z
DTEND;VALUE=DATE-TIME:20201023T121500Z
DTSTAMP;VALUE=DATE-TIME:20210124T161434Z
UID:BeijingMoscowColloquium/2
DESCRIPTION:Title: Additive divisor problem and Applications\nby Dmitry Fr
olenkov (Steklov Mathematical Institute of RAS) as part of Beijing Moscow
Mathematics Colloquium\n\n\nAbstract\nAdditive Divisor Problem (ADP) is co
ncerned with finding an asymptotic formula for the sum $\\sum_{n< X}d(n)d(
n+a)$\, where $d(n)=\\sum_{d|n}1$ is the divisor function. Surprisingly\,
the ADP arises naturally in quite different problems of number theory. For
example\, it is related to the investigation of the 4th moment of the Rie
mann zeta-function\, the second moment of automorphic L-functions and the
mean values of the length of continued fractions. In the talk\, I will des
cribe the ADP and its applications.\n\nMeeting ID：648 6454 8936 Password
：899678\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi Shi (Peking University)
DTSTART;VALUE=DATE-TIME:20201106T080000Z
DTEND;VALUE=DATE-TIME:20201106T090000Z
DTSTAMP;VALUE=DATE-TIME:20210124T161434Z
UID:BeijingMoscowColloquium/3
DESCRIPTION:Title: Spectrum rigidity and integrability for Anosov diffeomo
rphisms\nby Yi Shi (Peking University) as part of Beijing Moscow Mathemati
cs Colloquium\n\n\nAbstract\nLet $f$ be a partially hyperbolic derived-fro
m-Anosov diffeomorphism on 3-torus $\\mathbb{T}^3$. We show that the stabl
e and unstable bundle of $f$ is jointly integrable if and only if $f$ is A
nosov and admits spectrum rigidity in the center bundle. This proves the E
rgodic Conjecture on $\\mathbb{T}^3$.\n\nIn higher dimensions\, let $A\\in
{\\rm SL}(n\,\\mathbb{Z})$ be an irreducible hyperbolic matrix admitting c
omplex simple spectrum with different moduli\, then $A$ induces a diffeomo
rphism on $\\mathbb{T}^n$. We will also discuss the equivalence of integra
bility and spectrum rigidity for $f\\in{\\rm Diff}^2(\\mathbb{T}^n)$ which
is $C^1$-close to $A$.\n\nZoom Meeting ID: 674 4141 7410\nPassword: 90519
8\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Lokutsievskiy (Steklov Mathematical Institute of RAS)
DTSTART;VALUE=DATE-TIME:20201106T090000Z
DTEND;VALUE=DATE-TIME:20201106T100000Z
DTSTAMP;VALUE=DATE-TIME:20210124T161434Z
UID:BeijingMoscowColloquium/4
DESCRIPTION:Title: Аn application of algebraic topology and graph theory
in microeconomics\nby Lev Lokutsievskiy (Steklov Mathematical Institute of
RAS) as part of Beijing Moscow Mathematics Colloquium\n\n\nAbstract\nOne
of the important questions in mechanism design is the implementability of
allocation rules. An allocation rule is called implementable if for any ag
ent\, benefit from revealing its true type is better than benefit from lyi
ng. I’ll show some illustrative examples. Obviously\, some allocation ru
les are not implementable. Rochet’s theorem states that an allocation ru
le is implementable iff it is cyclically monotone. During the talk\, I’l
l present a new convenient topological condition that guarantees that cycl
ic monotonicity is equivalent to ordinary monotonicity. The last one is ea
sy to check (in contrary to cyclic one). Graph theory and algebraic topolo
gy appear to be very useful here.\n\nZoom Meeting ID: 674 4141 7410 \nPass
word: 905198\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taras Panov (Moscow State University)
DTSTART;VALUE=DATE-TIME:20201120T080000Z
DTEND;VALUE=DATE-TIME:20201120T090000Z
DTSTAMP;VALUE=DATE-TIME:20210124T161434Z
UID:BeijingMoscowColloquium/5
DESCRIPTION:Title: Right-angled polytopes\, hyperbolic manifolds and torus
actions\nby Taras Panov (Moscow State University) as part of Beijing Mosc
ow Mathematics Colloquium\n\n\nAbstract\nA combinatorial 3-dimensional pol
ytope $P$ can be realized in Lobachevsky 3-space with right dihedral angle
s if and only if it is simple\, flag and does not have 4-belts of facets.
This criterion was proved in the works of A. Pogorelov and E. Andreev of t
he 1960s. We refer to combinatorial 3 polytopes admitting a right-angled r
ealisation in Lobachevsky 3-space as Pogorelov polytopes. The Pogorelov cl
ass contains all fullerenes\, i.e. simple 3-polytopes with only 5-gonal an
d 6-gonal facets. There are two families of smooth manifolds associated wi
th Pogorelov polytopes. The first family consists of 3-dimensional small c
overs (in the sense of M. Davis and T. Januszkiewicz) of Pogorelov polytop
es $P$\, also known as hyperbolic 3-manifolds of Loebell type. These are a
spherical 3-manifolds whose fundamental groups are certain extensions of a
belian 2-groups by hyperbolic right-angled reflection groups in the facets
of $P$. The second family consists of 6-dimensional quasi toric manifolds
over Pogorelov polytopes. These are simply connected 6-manifolds with a 3
-dimensional torus action and orbit space $P$. Our main result is that bot
h families are cohomologically rigid\, i.e. two manifolds $M$ and $M'$ fro
m either family are diffeomorphic if and only if their cohomology rings ar
e isomorphic. We also prove that a cohomology ring isomorphism implies an
equivalence of characteristic pairs\; in particular\, the corresponding po
lytopes $P$ and $P'$ are combinatorially equivalent. This leads to a posit
ive solution of a problem of A. Vesnin (1991) on hyperbolic Loebell manifo
lds\, and implies their full classification. Our results are intertwined w
ith classical subjects of geometry and topology such as combinatorics of 3
-polytopes\, the Four Colour Theorem\, aspherical manifolds\, a diffeomorp
hism classification of 6-manifolds and invariance of Pontryagin classes. T
he proofs use techniques of toric topology. This is a joint work with V. B
uchstaber\, N. Erokhovets\, M. Masuda and S. Park.\n\nZoom Meeting ID: 626
6992 6224 Password: 363601\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi Liu (Beijing International Center for Mathematical Research)
DTSTART;VALUE=DATE-TIME:20201120T090000Z
DTEND;VALUE=DATE-TIME:20201120T100000Z
DTSTAMP;VALUE=DATE-TIME:20210124T161434Z
UID:BeijingMoscowColloquium/6
DESCRIPTION:Title: Finite covers of 3-manifolds\nby Yi Liu (Beijing Intern
ational Center for Mathematical Research) as part of Beijing Moscow Mathem
atics Colloquium\n\n\nAbstract\nIn this talk\, I will discuss some develop
ments in 3-manifold topology of this century regarding finite covering spa
ces. These developments led to the resolution of Thurston's virtual Haken
conjecture and other related conjectures around 2012. Since then\, people
have been seeking for new applications of those techniques and their combi
nation with other branches of mathematics.\n\nZoom Meeting ID: 626 6992 62
24 Password: 363601\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Gaifullin (Steklov Mathematical Institute of RAS)
DTSTART;VALUE=DATE-TIME:20201204T080000Z
DTEND;VALUE=DATE-TIME:20201204T090000Z
DTSTAMP;VALUE=DATE-TIME:20210124T161434Z
UID:BeijingMoscowColloquium/7
DESCRIPTION:Title: On homology of Torelli groups\nby Alexander Gaifullin (
Steklov Mathematical Institute of RAS) as part of Beijing Moscow Mathemati
cs Colloquium\n\n\nAbstract\nThe mapping class groups of oriented surfaces
are important examples of groups whose properties are closely related to
geometry and topology of moduli spaces\, topology of 3-manifolds\, automor
phisms of free groups. The mapping class group of a closed oriented surfac
e contains two important subgroups\, the Torelli group\, which consists of
all mapping classes that act trivially on the homology of the surface\, a
nd the Johnson kernel\, which is the subgroup generated by all Dehn twists
about separating curves. The talk will be devoted to results on homology
of these two subgroups. Namely\, we will show that the $k$-dimensional hom
ology group of the genus g Torelli group is not finitely generated\, provi
ded that k is in range from $2g-3$ and $3g-5$ (the case $3g-5$ was previou
sly known by a result of Bestvina\, Bux\, and Margalit)\, and the $(2g-3)$
-dimensional homology group the genus g Johnson kernel is also not finitel
y generated. The proof is based on a detailed study of the spectral sequen
ces associated with the actions of these groups on the complex of cycles c
onstructed by Bestvina\, Bux\, and Margalit.\n\nZoom Meeting ID: 668 8175
3105\nPassword: 348558\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guozhen Wang (Shanghai Center for Mathematical Sciences\, Fudan Un
iversity)
DTSTART;VALUE=DATE-TIME:20201204T090000Z
DTEND;VALUE=DATE-TIME:20201204T100000Z
DTSTAMP;VALUE=DATE-TIME:20210124T161434Z
UID:BeijingMoscowColloquium/8
DESCRIPTION:Title: Stable homotopy groups of spheres\nby Guozhen Wang (Sha
nghai Center for Mathematical Sciences\, Fudan University) as part of Beij
ing Moscow Mathematics Colloquium\n\n\nAbstract\nWe will discuss the curre
nt state of knowledge of stable homotopy groups of spheres. We describe a
computational method using motivic homotopy theory\, viewed as a deformati
on of classical homotopy theory. This yields a streamlined computation of
the first 61 stable homotopy groups and gives information about the stable
homotopy groups in dimensions 62 through 90. As an application\, we deter
mine the groups of homotopy spheres that classify smooth structures on sph
eres through dimension 90\, except for dimension 4. The method relies more
heavily on machine computations than previous methods and is therefore le
ss prone to error. The main mathematical tool is the Adams spectral sequen
ce.\n\nZoom Meeting ID: 668 8175 3105 Password: 348558\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhifei Zhang (School of Mathematical Sciences\, Peking University)
DTSTART;VALUE=DATE-TIME:20210115T080000Z
DTEND;VALUE=DATE-TIME:20210115T090000Z
DTSTAMP;VALUE=DATE-TIME:20210124T161434Z
UID:BeijingMoscowColloquium/9
DESCRIPTION:Title: Linear stability of pipe Poiseuille flow at high Reynol
ds number regime\nby Zhifei Zhang (School of Mathematical Sciences\, Pekin
g University) as part of Beijing Moscow Mathematics Colloquium\n\n\nAbstra
ct\nThe linear stability of pipe Poiseuille flow is a long standing proble
m since Reynolds experiment in 1883. Joint with Qi Chen and Dongyi Wei\, w
e solve this problem at high Reynolds regime. We first introduce a new for
mulation for the linearized 3-D Navier-Stokes equations around this flow.
Then we establish the resolvent estimates of this new system under favorab
le artificial boundary conditions. Finally\, we solve the original system
by constructing a boundary layer corrector.\n\nMeeting ID：645 2363 5960\
nPassword：714716\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir E. Nazaikinskii (Ishlinsky Institute for Problems in Mech
anics RAS)
DTSTART;VALUE=DATE-TIME:20210115T090000Z
DTEND;VALUE=DATE-TIME:20210115T100000Z
DTSTAMP;VALUE=DATE-TIME:20210124T161434Z
UID:BeijingMoscowColloquium/10
DESCRIPTION:Title: Partial spectral flow and the Aharonov-Bohm effect in g
raphene\nby Vladimir E. Nazaikinskii (Ishlinsky Institute for Problems in
Mechanics RAS) as part of Beijing Moscow Mathematics Colloquium\n\n\nAbstr
act\nWe study the Aharonov-Bohm effect in an open-ended tube made of a gra
phene sheet whose dimensions are much larger than the interatomic distance
in graphene. An external magnetic field vanishes on and in the vicinity o
f the graphene sheet\, and its flux through the tube is adiabatically swit
ched on. It is shown that\, in the process\, the energy levels of the tigh
t-binding Hamiltonian of $\\pi$-electrons unavoidably cross the Fermi leve
l\, which results in the creation of electron-hole pairs. The number of pa
irs is proven to be equal to the number of magnetic flux quanta of the ext
ernal field. The proof is based on the new notion of partial spectral flow
\, which generalizes the ordinary spectral flow introduced by Atiyah\, Pat
odi\, and Singer and already having well-known applications (such as the K
opnin forces in superconductors and superfluids) in condensed matter physi
cs.\n\nMeeting ID：645 2363 5960\nPassword：714716\n
END:VEVENT
END:VCALENDAR