BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Eivind Schneider (Hradec Kralove University)
DTSTART;VALUE=DATE-TIME:20200415T093000Z
DTEND;VALUE=DATE-TIME:20200415T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/1
DESCRIPTION:Title: Differential invariants in thermodynamics\nby Eivind Sc
hneider (Hradec Kralove University) as part of Prague-Hradec Kralove semin
ar Cohomology in algebra\, geometry\, physics and statistics\n\nLecture he
ld in ZOOM meeting ID 895-276-2498.\n\nAbstract\nIt is well known that
contact geometry gives the appropriate framework for formulating thermodyn
amics: Thermodynamic states can be interpreted as Legendrian submanifolds
of a certain contact manifold. The existence of a metric on thermodynamic
states has also received some attention in the last decades. The metric ca
n be interpreted as the variance of an underlying probability measure. Les
s studied is the action of the affine group that appears naturally in this
context as the group preserving the variance. We study this group action
by finding generators of its algebra of scalar differential invariants\, w
hich intuitively can be thought of as the observables in the theory. In th
e end\, we discuss the relation between the invariants and some well-known
physical quantities in thermodynamics.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Galaev (Hradec Kralove University)
DTSTART;VALUE=DATE-TIME:20200422T093000Z
DTEND;VALUE=DATE-TIME:20200422T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/2
DESCRIPTION:Title: Non-diffeomorphic Reeb foliations and modified Godbillon-Ve
y class\nby Anton Galaev (Hradec Kralove University) as part of Prague
-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and sta
tistics\n\n\nAbstract\nThe definition of the Reeb foliation depends upon t
wo real functions satisfying certain conditions. All these foliations are
pairwise homeomorphic and have trivial Godbillon-Vey class. We construct e
xplicit examples of the Reeb foliations that are not diffeomorphic. For th
is purpose we show that a modified Godbillon-Vey class defined by Losik is
non-trivial for some Reeb foliations and trivial for some other Reeb foli
ations. This characteristic class takes values in the second order frame b
undle of the leaf space of the foliation. This is a joint work with Ya. Ba
zaikin and P. Gumenyuk.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Khavkine (Institute of Mathematics\, Czech Academy of Scien
ces)
DTSTART;VALUE=DATE-TIME:20200429T093000Z
DTEND;VALUE=DATE-TIME:20200429T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/3
DESCRIPTION:Title: Triangular decoupling of systems of differential equations\
, with application to separation of variables on Schwarzschild spacetime\nby Igor Khavkine (Institute of Mathematics\, Czech Academy of Scienc
es) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geome
try\, physics and statistics\n\n\nAbstract\nCertain tensor wave equations
admit a complete separation of variables on the Schwarzschild spacetime (s
tatic\, spherically symmetric black hole)\, resulting in complicated syste
ms of radial mode ODEs. The spectral theory of these systems has important
applications to the stability analysis electromagnetic and gravitational
perturbations of the black hole. However\, almost none of the important qu
estions about the radial mode equations can be answered in their original
form. I will discuss a drastic simplification of these ODE systems to spar
se upper triangular form that is directly susceptible to spectral analysis
. Essential to this simplification are geometric properties of the origina
l tensor wave equations\, ideas from homological algebra and from the theo
ry of ODEs with rational coefficients. Based on [arXiv:1711.00585\, 1801.0
9800\, 2004.09651]\n\nPlease contact the speaker or an organizer to get Zo
om livestream access information.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Roop (Moscow State University)
DTSTART;VALUE=DATE-TIME:20200506T093000Z
DTEND;VALUE=DATE-TIME:20200506T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/4
DESCRIPTION:Title: Shock waves in Euler flows of gases\nby Mikhail Roop (M
oscow State University) as part of Prague-Hradec Kralove seminar Cohomolog
y in algebra\, geometry\, physics and statistics\n\n\nAbstract\nWe study n
on-stationary 1-dimensional flows of gases described by a quasilinear syst
em of differential equations including Euler equation and continuity equat
ion. We show that equations in question essentially depend on thermodynami
cs of the medium. We represent the system by means of 2-forms on zero-jet
space and get some exact solutions by means of such a representation. The
solutions obtained are multivalued\, we find caustics and shock wave front
. The method can be applied to any thermodynamic state of the medium as we
ll as to any thermodynamic process. The talk is based on our joint paper w
ith Valentin Lychagin\, arXiv:2004.05015.\n\nPlease contact the speaker or
an organizer to get Zoom livestream access information.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Kotov (University Hradec Kralove)
DTSTART;VALUE=DATE-TIME:20200513T093000Z
DTEND;VALUE=DATE-TIME:20200513T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/5
DESCRIPTION:Title: Geometry of gauge PDEs I\nby Alexei Kotov (University H
radec Kralove) as part of Prague-Hradec Kralove seminar Cohomology in alge
bra\, geometry\, physics and statistics\n\n\nAbstract\nI will show how jet
spaces and Q-bundles can be incorporated into an invariant mathematical d
escription of gauge theories.\n\nPlease contact the speaker or an organize
r to get Zoom livestream access information.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Positselski (Institute of Mathematics\, Czech Academy of Sc
iences)
DTSTART;VALUE=DATE-TIME:20200401T093000Z
DTEND;VALUE=DATE-TIME:20200401T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/6
DESCRIPTION:Title: Koszul algebras and one-dependent random 0-1 sequences\
nby Leonid Positselski (Institute of Mathematics\, Czech Academy of Scienc
es) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geome
try\, physics and statistics\n\n\nAbstract\nKoszul algebras are a natural
class of graded algebras with\nquadratic relations\, defined by a series o
f homological conditions.\nTo a Koszul algebra over a field with finite-di
mensional components\,\none can assign a one-dependent stochastic 0-1 sequ
ence\, which carries\ninformation about the dimensions of the algebra's gr
ading components.\nThis construction allows to show that the Hilbert serie
s of a Koszul\nalgebra can be extended meromorphically to the circle of do
uble radius.\nConjecturally\, such Hilbert series are meromorphic in the w
hole\ncomplex plane (and consequently\, rational).\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Kotov (University Hradec Kralove)
DTSTART;VALUE=DATE-TIME:20200520T093000Z
DTEND;VALUE=DATE-TIME:20200520T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/7
DESCRIPTION:Title: Geometry of gauge PDEs II\nby Alexei Kotov (University
Hradec Kralove) as part of Prague-Hradec Kralove seminar Cohomology in alg
ebra\, geometry\, physics and statistics\n\n\nAbstract\nI will show how je
t spaces and Q-bundles can be incorporated into an invariant mathematical
description of gauge theories.\n\n(This is a continuation of Alexei Koto
v's seminar from last week.)\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luigi Caputi (Institute of Informatics of the Czech Academy of Sci
ences)
DTSTART;VALUE=DATE-TIME:20200610T093000Z
DTEND;VALUE=DATE-TIME:20200610T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/8
DESCRIPTION:Title: Cyclic homology for bornological coarse spaces\nby Luig
i Caputi (Institute of Informatics of the Czech Academy of Sciences) as pa
rt of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, phy
sics and statistics\n\n\nAbstract\nBornological coarse spaces are "large s
cale"\ngeneralizations of metric spaces (up to quasi-isometry). Homologica
l\ninvariants of such spaces are given by coarse homology theories\, which
\nare functors from the category of bornological coarse spaces to a stable
\ncocomplete ∞-category\, satisfying additional axioms. Among the main\n
examples of coarse homology theories\, there are coarse versions of\nordin
ary homology\, of topological\nand algebraic K-theory. In the talk we defi
ne G-equivariant coarse\nversions of the classical Hochschild and cyclic h
omologies (of\nalgebras). If k is a field\, the evaluation at the one poin
t space\ninduces equivalences with the classical Hochschild and cyclic hom
ology\nof k. In the equivariant setting\, the G-equivariant coarse Hochsch
ild\n(cyclic) homology of the discrete group G agrees with the classical\n
Hochschild (cyclic) homology of the associated group algebra k[G].\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vojtech Pravda (Institute of Mathematics of the Czech Academy of S
ciences)
DTSTART;VALUE=DATE-TIME:20200527T093000Z
DTEND;VALUE=DATE-TIME:20200527T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/9
DESCRIPTION:Title: Universal\, almost universal and related spacetimes\nby
Vojtech Pravda (Institute of Mathematics of the Czech Academy of Sciences
) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geometr
y\, physics and statistics\n\n\nAbstract\nFor universal spacetimes\, all r
ank-2 tensors constructed from the metric\, Riemann tensors\, and its cova
riant derivatives of arbitrary order are proportional to the metric. Conse
quently\, all vacuum field equations of generalized theories of gravity fo
llowing from Lagrangian constructed from the Riemann tensors and its covar
iant derivatives of arbitrary order are simultaneously satisfied. We will
present necessary and sufficient conditions for several classes of univers
al spacetimes of Lorentzian signature\, some explicit examples of such spa
cetimes\, and discuss certain useful generalizations of the universal prop
erty.\n\nContact an organizer or the speaker for Zoom connection details.
Virtual coffee starts already at 11:00 before the seminar.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petr Somberg (Charles University Prague)
DTSTART;VALUE=DATE-TIME:20200603T093000Z
DTEND;VALUE=DATE-TIME:20200603T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/10
DESCRIPTION:Title: An approach to the representation theory of symmetric grou
ps\nby Petr Somberg (Charles University Prague) as part of Prague-Hrad
ec Kralove seminar Cohomology in algebra\, geometry\, physics and statisti
cs\n\n\nAbstract\nWe give an expository account of Vershik-Okounkov approa
ch to the representation theory of symmetric groups (based on the Gelfand-
Tsetlin basis and the Young-Jucys-Murphy elements.) If time permits\, we e
xplain some geometrical problems which lead to certain conjectural stateme
nts generalizing V-O approach.\n\nContact an organizer or the speaker for
Zoom connection details. Virtual coffee starts already at 11:00 before the
seminar.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Zuevsky (Institute of Mathematics of the Czech Academy o
f Sciences)
DTSTART;VALUE=DATE-TIME:20200617T093000Z
DTEND;VALUE=DATE-TIME:20200617T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/11
DESCRIPTION:Title: Vertex algebra cohomology of foliations on Riemann surface
s\nby Alexander Zuevsky (Institute of Mathematics of the Czech Academy
of Sciences) as part of Prague-Hradec Kralove seminar Cohomology in algeb
ra\, geometry\, physics and statistics\n\n\nAbstract\nIn the transversal b
asis formalism\, we construct a vertex algebra cochain complex\, show its
independence on coordinates and choice of basis\, and define the vertex al
gebra cohomology for a foliation on a smooth complex curve. The first coho
mologies are determined in terms of connections and classes of extensions
of the vertex algebra. We will introduce the cohomological class\, conside
r the main example of $\\operatorname{Re} \\omega=0$ foliation on a Rieman
n surface\, and make a connection with considerations of other codimension
one examples.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen J. Watson (School of Mathematics & Statistics\, University
of Glasgow)
DTSTART;VALUE=DATE-TIME:20200624T093000Z
DTEND;VALUE=DATE-TIME:20200624T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/12
DESCRIPTION:Title: Lorentzian Symmetry Predicts Universality Beyond Power Law
s\nby Stephen J. Watson (School of Mathematics & Statistics\, Universi
ty of Glasgow) as part of Prague-Hradec Kralove seminar Cohomology in alge
bra\, geometry\, physics and statistics\n\n\nAbstract\nThe statistical phy
sics governing phase-ordering dynamics following a symmetry breaking first
-order phase transition is an area of active research. The Coarsening/Agei
ng of the ensemble of phase domains\, wherein irreversible annihilation o
r joining of domains yields a growing characteristic domain length\, is a
omniprescent feature whose universal characteristics one would wish to und
erstand. Driven kinetic Ising models and growing nano-faceted crystals are
theoretically important examples of such Coarsening (Ageing) Dynamical Sy
stems (CDS)\, since they additionally break thermodynamic fluctuation-diss
ipation relations.\nPower-laws for the growth in time of the characteristi
c size of domains (e.g.\, lengths) of CDS\, and a concomitant {\\em scale
-invariance} of the associated length distributions\, has so frequently b
een empirically observed that their presence has acquired the status of a
principle\; the so-called Dynamic-Scaling Hypothesis. \nBut the dynamical
symmetries of a given CDS- its Coarsening Group $G$ - may include more tha
n the global spatio-temporal scalings underlying the {\\em Dynamic Scaling
Hypothesis}. \nIn this talk\, I will present a recently developed theoret
ical framework (Ref.[1]) that shows how the symmetry group G of a Coarseni
ng (ageing) Dynamical System (CDS) necessarily yields G-equivariance (cova
riance) of the CDS's universal statistical observables. We exhibit this t
heory for a variety of model systems\, of both thermodynamic and driven ty
pe\, with symmetries that may also be {/em emergent} (Ref. [2\,3]) and/or
{\\em hidden}. We will close with a magical theoretical coarsening law whi
ch reflects Lorentzian and parabolic symmetries!\n\n\nReferences:\n\n[1] L
orentzian symmetry predicts universality beyond scaling laws\,\nSJ Watson\
, EPL 118 (5)\, 56001\, (Aug.2\, 2017)\, Editor's Choice\nhttp://iopscienc
e.iop.org/article/10.1209/0295-5075/118/56001/meta\n\n[2] Emergent parabol
ic scaling of nano-faceting crystal growth\,\nStephen J. Watson\, Proc. R
. Soc. A 471: 20140560 (2015)\nhttp://rspa.royalsocietypublishing.org/cont
ent/471/2174/20140560\n\n[3] Scaling Theory and Morphometrics for a Coarse
ning Multiscale Surface\, via a Principle of Maximal Dissipation\,\nStephe
n J. Watson and Scott A. Norris\, Phys. Rev. Lett. 96\, 176103 (2006)\nhtt
p://journals.aps.org/prl/abstract/10.1103/PhysRevLett.96.176103\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Golovko (Charles University)
DTSTART;VALUE=DATE-TIME:20201007T093000Z
DTEND;VALUE=DATE-TIME:20201007T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/13
DESCRIPTION:Title: On the different perspective of the Casals-Murphy criterio
n of looseness\nby Roman Golovko (Charles University) as part of Pragu
e-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and st
atistics\n\n\nAbstract\nWe show that inside a trivial open book $\\partial
(W\\times D^2)$ with page being a Weinstein manifold $(W\, d\\theta)$\, a
ny Legendrian which is contained entirely inside a page and which intersec
ts some cocore disc transversely in a single point is loose. This leads to
the alternative proof of Casals-Murphy criterion of looseness. This is jo
int work with Georgios Dimitroglou Rizell.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Cattafi (KU Leuven)
DTSTART;VALUE=DATE-TIME:20201014T093000Z
DTEND;VALUE=DATE-TIME:20201014T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/14
DESCRIPTION:Title: Formal integrability of geometric structures\nby Franc
esco Cattafi (KU Leuven) as part of Prague-Hradec Kralove seminar Cohomolo
gy in algebra\, geometry\, physics and statistics\n\n\nAbstract\nA Γ-stru
cture on a manifold is a maximal atlas whose changes of coordinates take v
alues in a Lie pseudogroup Γ. Various geometric structures (e.g. symplect
ic\, complex and contact structures) fit in this framework\, but there is
no general definition of almost Γ-structure (e.g. almost symplectic\, alm
ost complex and almost contact structures) in terms of Γ. In this talk we
are going to fill this gap by introducing the general definition of an al
most Γ-structure\, and presenting a characterisation of its formal integr
ability. This will be obtained by introducing the concept of principal Pfa
ffian bundle. We will draw inspiration from the theory of PDEs\, from Pois
son geometry\, as well as from similar results in the theory of G-structur
es\, which we recover as particular cases. This is joint work with Marius
Crainic.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Domenico Fiorenza (Università di Roma “La Sapienza”)
DTSTART;VALUE=DATE-TIME:20201021T093000Z
DTEND;VALUE=DATE-TIME:20201021T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/15
DESCRIPTION:Title: Formally integrable complex structures on higher dimension
al knot spaces\nby Domenico Fiorenza (Università di Roma “La Sapien
za”) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, ge
ometry\, physics and statistics\n\n\nAbstract\nBy the Brown-Gray’s class
ification\, there are four classes of Riemannian manifolds $M$ with parall
el $r$-fold vector cross products: $r = 1$ and $M$ a Kähler manifold\, $r
= \\dim M − 1$\, $r = 2$ and $M$ a $G_2$-manifold\, $r = 3$ and $M$ a $
Spin(7)$-manifold. For the first three classes it has been proven by Bryli
nski\, LeBrun\, and Verbitsky\, via ad hoc arguments for each of these cla
sses\, that the higher knot spaces for $M$ carry a natural formally Kähle
r structure. More recently\, Henrich provided a new proof for the $r = \\d
im M − 1$ case. In a recent work with Hông Vân Lê (arXiv:1912.05175)\
, we show how a variant of Henrich's construction can be used to provide a
uniform proof for all four classes. In particular\, this provides a proof
for the previously unknown case of $Spin(7)$-manifolds.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zoran Skoda (University of Zadar and University of Hradec Kralove)
DTSTART;VALUE=DATE-TIME:20201104T103000Z
DTEND;VALUE=DATE-TIME:20201104T113000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/17
DESCRIPTION:Title: Gluing bundles over noncommutative flag varieties\nby
Zoran Skoda (University of Zadar and University of Hradec Kralove) as part
of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physi
cs and statistics\n\n\nAbstract\nLocalization functors may be used to defi
ne local covers in some\nexamples from noncommutative geometry. In an earl
ier work\, I have used\nthis technique to treat\ngluing of bundles over qu
antum flag varieties with applications to quantum group\ncoherent states a
nd representation theory. A non-flat version of this technique\nis under d
evelopment. A basic series of examples is what I call\nuniversal noncommut
ative flag varieties (including Grassmannians)\,\nwhere no "quantum" relat
ions are imposed.\nVarious classical and quantum flag varieties appear as
subvarieties. I will\npresent these the rationale behind these examples an
d of gluing technique\nfor certain special covers. Main aim is to derive e
xplicit cocycle describing\ncertain tautological bundle over a universal n
oncommutative Grassmannian\nleading to noncommutative double ratios studie
d recently\nby Retakh\, Rubtsov and Sharygin.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tat Dat To (UPMC Paris VI)
DTSTART;VALUE=DATE-TIME:20201118T103000Z
DTEND;VALUE=DATE-TIME:20201118T113000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/18
DESCRIPTION:Title: Convergence of the Kähler-Ricci flow on varieties of gene
ral type\nby Tat Dat To (UPMC Paris VI) as part of Prague-Hradec Kralo
ve seminar Cohomology in algebra\, geometry\, physics and statistics\n\n\n
Abstract\nWe study the Kähler-Ricci flow on varieties of general type. We
show that the normalized Kähler-Ricci flow exists at all times in the se
nse of viscosity\, is continuous in an open Zariski set and converges to t
he singular Kähler-Einstein metric. This gives an answer to a question of
Feldman-Ilmanen-Knopf.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfonso Tortorella (KU Leuven)
DTSTART;VALUE=DATE-TIME:20210106T103000Z
DTEND;VALUE=DATE-TIME:20210106T113000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/19
DESCRIPTION:Title: Deformations of symplectic foliations\nby Alfonso Tort
orella (KU Leuven) as part of Prague-Hradec Kralove seminar Cohomology in
algebra\, geometry\, physics and statistics\n\n\nAbstract\nIn this talk\,
based on joint work with Stephane Geudens and Marco Zambon\, I develop the
deformation theory of symplectic foliations\, i.e. regular foliations equ
ipped with a leaf-wise symplectic form. The main result is that each sympl
ectic foliation is attached with an $L_\\infty$ algebra controlling its de
formation problem. Indeed\, we establish a one-to-one correspondence betwe
en the small deformations of a given symplectic foliation and the MC eleme
nts of the associated $L_\\infty$ algebra. Further\, we prove that\, under
this one-to-one correspondence\, the equivalence by isotopies of symplect
ic foliations agrees with the gauge equivalence of MC elements. Finally\,
we show that the infinitesimal deformations of symplectic foliations can b
e obstructed.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mahir Can (Tulane University)
DTSTART;VALUE=DATE-TIME:20201209T104500Z
DTEND;VALUE=DATE-TIME:20201209T114500Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/20
DESCRIPTION:Title: Quotients of Classical Symmetric Spaces\nby Mahir Can
(Tulane University) as part of Prague-Hradec Kralove seminar Cohomology in
algebra\, geometry\, physics and statistics\n\n\nAbstract\nIn this talk w
e will discuss some new and old results regarding the wonderful embeddings
of classical complex symmetric spaces. More precisely\, we will introduce
certain (non-arithmetic) quotients of classical symmetric spaces. Then w
e will describe their combinatorial and geometric properties in relation w
ith their wonderful embeddings. Our running example will be on the variety
of nondegenerate quadrics.\n\nNB: Start time 15 later than usual. Virtual
coffee starts on Zoom already at 11:30 before the seminar.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Alexandrov (IBS\, Center for Geometry and Physics\, Poha
ng)
DTSTART;VALUE=DATE-TIME:20201202T103000Z
DTEND;VALUE=DATE-TIME:20201202T113000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/21
DESCRIPTION:Title: KP integrability of triple Hodge integrals\nby Alexand
er Alexandrov (IBS\, Center for Geometry and Physics\, Pohang) as part of
Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics a
nd statistics\n\n\nAbstract\nIn my talk I will describe a relation between
the Givental group of rank one and Heisenberg-Virasoro symmetry group of
the KP integrable hierarchy. In particular I will show that only a two-par
ameter family of the Givental operators can be identified with elements of
the Heisenberg-Virasoro symmetry group. This family describes triple Hodg
e integrals satisfying the Calabi-Yau condition. Using identification of t
he elements of two groups it is possible to prove that the generating func
tion of triple Hodge integrals satisfying the Calabi-Yau condition and its
$\\Theta$-version are tau-functions of the KP hierarchy. This generalizes
the result of Kazarian on KP integrability in case of linear Hodge integr
als. I will also describe the relation of this family of tau-functions wit
h the generalized Kontsevich matrix model. My talk is based on two papers\
, arXiv:2009.01615 and arXiv:2009.10961.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Hajek (University Hamburg)
DTSTART;VALUE=DATE-TIME:20201216T103000Z
DTEND;VALUE=DATE-TIME:20201216T113000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/22
DESCRIPTION:Title: Chain models of string topology coming from symplectic geo
metry\nby Pavel Hajek (University Hamburg) as part of Prague-Hradec Kr
alove seminar Cohomology in algebra\, geometry\, physics and statistics\n\
n\nAbstract\nI will recall loop spaces\, natural structures on their homol
ogy and the relation to symplectic geometry of the cotangent bundle (speci
fically to chain level structures defined by counting holomorphic curves).
I will then zoom in on the equivariant case and a chain model based on de
Rham forms and Chern-Simons theory. I will show some computations and exp
lain how this structure appears in various contexts.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Schenkel (University of Nottingham)
DTSTART;VALUE=DATE-TIME:20210113T103000Z
DTEND;VALUE=DATE-TIME:20210113T113000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/23
DESCRIPTION:Title: Boundary conditions and edge modes in gauge theories\n
by Alexander Schenkel (University of Nottingham) as part of Prague-Hradec
Kralove seminar Cohomology in algebra\, geometry\, physics and statistics\
n\n\nAbstract\nThe fields of a classical gauge theory form a smooth groupo
id (aka stack) with morphisms given by gauge transformations. From this pe
rspective\, the concept of "equality" of two gauge fields $A$ and $A'$ is
not a property but rather additional data given by the choice of a gauge t
ransformation $A \\to A'$ which witnesses that $A$ and $A'$ are "the same"
. In this talk\, I will explain how this higher-categorical point of view
is useful to study gauge theories on manifolds with boundaries and defects
. In particular\, I will show that the additional data witnessing boundary
conditions are precisely the famous edge modes from physics. As examples\
, I will discuss 3d Abelian Chern-Simons theory on manifolds with boundary
\, which is physically describing the quantum Hall system\, and also the 4
d holomorphic Chern-Simons theory of Costello and Yamazaki where the edge
modes on surface defects determine 2d integrable field theories.\n\nThis t
alk is based on arXiv:1907.1065
1 and arXiv:2008.01829.
\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wilderich Tuschmann (Karlsruhe Institute of Technology)
DTSTART;VALUE=DATE-TIME:20210224T103000Z
DTEND;VALUE=DATE-TIME:20210224T113000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/24
DESCRIPTION:Title: (MODULI) SPACES OF RIEMANNIAN METRICS\nby Wilderich Tu
schmann (Karlsruhe Institute of Technology) as part of Prague-Hradec Kralo
ve seminar Cohomology in algebra\, geometry\, physics and statistics\n\n\n
Abstract\nConsider a smooth manifold with a Riemannian metric satisfying s
ome sort of curvature constraint like\, for example\, positive scalar curv
ature\, non-negative Ricci or negative sectional curvature\, being Einstei
n\, Kähler\, Sasaki\, etc. A natural question to study is then what the s
pace of all such metrics does look like. Moreover\, one can also pose this
question for corresponding moduli spaces of metrics\, i.e.\, quotients of
the former by (suitable subgroups of) the diffeomorphism group of the man
ifold\, acting by pulling back metrics.\n\nThese spaces are customarily eq
uipped with the topology of smooth convergence on compact subsets and the
quotient topology\, respectively\, and their topological properties then p
rovide the right means to measure 'how many' different metrics and geometr
ies the given manifold actually does exhibit\; but one can topologize and
view those also in very different manners.\n\nIn my talk\, I will report o
n some general results and open questions about spaces and moduli spaces o
f metrics with a focus on non-negative Ricci or sectional curvature as wel
l as other lower curvature bounds on closed and open manifolds\, and\, in
particular\, also discuss broader non-traditional approaches from metric g
eometry and analysis to these objects and topics.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Gregorovic (University Hradec Kralove)
DTSTART;VALUE=DATE-TIME:20210317T103000Z
DTEND;VALUE=DATE-TIME:20210317T113000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/26
DESCRIPTION:Title: First BGG operators on homogeneous parabolic geometries\nby Jan Gregorovic (University Hradec Kralove) as part of Prague-Hradec
Kralove seminar Cohomology in algebra\, geometry\, physics and statistics\
n\n\nAbstract\nI will briefly review the theory of BGG operators on parabo
lic geometries and show\, how to construct and find (normal) solutions of
first BGG operators on homogeneous parabolic geometries\, in detail. In pa
rticular\, such a solution can be obtained by purely algebraic computation
s and using representation theory. This simplifies a construction of examp
les of BGG operators on nonflat homogeneous parabolic geometries admitting
nontrivial solutions\, which otherwise appear only rarely in the literatu
re. I will present one of such examples in CR geometry with nontrivial sol
utions for subriemannian metrizability among others.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Zuevsky (Institute of Mathematics of the Czech Academy o
f Sciences)
DTSTART;VALUE=DATE-TIME:20210324T103000Z
DTEND;VALUE=DATE-TIME:20210324T113000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/27
DESCRIPTION:Title: Reduction cohomology on complex manifolds\nby Alexande
r Zuevsky (Institute of Mathematics of the Czech Academy of Sciences) as p
art of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, ph
ysics and statistics\n\n\nAbstract\nDeveloping ideas of classical work of
Feigin\, and its development by Wagemann\,\nand proceed with a generalizat
ion of ideas of above works. We describe the\nnotion of a cohomology theor
y of infinite formal series with non-commutative\nmodes and localization o
f variables on Riemann surfaces\, constructed via\ncharacteristic function
s reduction formulas. We will mention algebraic\nconditions leading to cha
in property of complexes for characteristic functions\,\nand represent fur
ther restrictions on modular form coefficients in reduction formulas.\nRel
ations of reduction cohomologies to analytic continuations of Knizhnik-Zam
olodchikov\nequations as well as an example of application of Bott-Segal t
heorem will also be mentioned.\nJacobi forms case example will be consider
ed.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georgy Sharygin (Moscow State University Lomonosov)
DTSTART;VALUE=DATE-TIME:20210331T093000Z
DTEND;VALUE=DATE-TIME:20210331T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/28
DESCRIPTION:Title: Around the noncommutative cross ratio\nby Georgy Shary
gin (Moscow State University Lomonosov) as part of Prague-Hradec Kralove s
eminar Cohomology in algebra\, geometry\, physics and statistics\n\n\nAbst
ract\nThe cross-ratio of four points on a projective line is one of the mo
st important projective invariants\, which finds most unexpected applicati
ons throughout Mathematics from Geometry and Topology to the Integrable sy
stems theory. I will tell\, how one can widen the domain on which this inv
ariant is defined so as to allow one consider "projective lines" over nonc
ommutative field. It turns out that there is an approach\, which allows on
e find such generalization so that most of important properties of the cro
ss ratio are preserved. Study of this new object is an interesting new pro
blem. Based on joint work with V.Retakh and V.Rubtsov.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Fritz (University of Innsbruck\, Austria)
DTSTART;VALUE=DATE-TIME:20210407T093000Z
DTEND;VALUE=DATE-TIME:20210407T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/29
DESCRIPTION:Title: The de Finetti theorem in categorical probability\nby
Tobias Fritz (University of Innsbruck\, Austria) as part of Prague-Hradec
Kralove seminar Cohomology in algebra\, geometry\, physics and statistics\
n\n\nAbstract\nWhile probability theory is traditionally based on measure
theory and Kolmogorov's axioms as a foundation\, the recently proposed fo
rmalism of Markov categories constitutes a potential alternative approach
in which a (modest) number of classical theorems of probability and statis
tics have already been reproduced and generalized. In this talk\, I will i
ntroduce this approach and illustrate its utility by providing a statement
and proof of the classical de Finetti theorem in entirely abstract catego
rical terms without measure theory. Based on joint work with Tomáš Gonda
\, Paolo Perrone and Eigil Rischel.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Benini (University of Genoa)
DTSTART;VALUE=DATE-TIME:20210414T093000Z
DTEND;VALUE=DATE-TIME:20210414T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/30
DESCRIPTION:Title: Smooth 1-dimensional algebraic quantum field theories\
nby Marco Benini (University of Genoa) as part of Prague-Hradec Kralove se
minar Cohomology in algebra\, geometry\, physics and statistics\n\n\nAbstr
act\nAlgebraic quantum field theory (AQFT) axiomatizes quantum field theor
ies (QFTs) as functors A assigning to each spacetime M an algebra A(M)\, i
nterpreted as the algebra of observables of a QFT over the spacetime M. To
support this physical interpretation\, certain physical axioms are impose
d on the functors A. None of these axioms\, however\, addresses the follow
ing physically desirable feature: given a "smooth" family M_s of spacetime
s\, the family of algebras of observables A(M_s) should depend "smoothly"
on the parameter s in an appropriate sense. (Speaking even more loosely\,
a "mild variation" of the geometry of spacetime should determine a "mild v
ariation" of the algebra of observables.) The purpose of this talk is to p
resent a framework\, based on stacks of categories\, that allows for the s
mooth refinement of AQFTs mentioned above. To illustrate this framework\,
we will explore in detail the case of smooth 1-dimensional AQFTs. (Based o
n arXiv:2010.13808 [math-ph].)\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Reiterer (Berner Fachhochschule\, Switzerland)
DTSTART;VALUE=DATE-TIME:20210421T093000Z
DTEND;VALUE=DATE-TIME:20210421T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/31
DESCRIPTION:Title: Filtered expansions in general relativity\nby Michael
Reiterer (Berner Fachhochschule\, Switzerland) as part of Prague-Hradec Kr
alove seminar Cohomology in algebra\, geometry\, physics and statistics\n\
n\nAbstract\nI will review the BKL (Belinskii-Khalatnikov-Lifshitz) propos
al for singularities in general relativity\, for spatially homogeneous and
spatially inhomogeneous spacetimes. Then I will discuss a construction of
formal power series solutions\, for one BKL bounce\, which is a building
block for the BKL proposal. I will in particular highlight the algebraic t
ools that we use\, namely Maurer-Cartan perturbation theory and a filtrati
on that organizes the calculations. Joint with Eugene Trubowitz\, see arXiv:1905.09026 and arXiv:2005.03390.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jérémie Joudioux (Albert Einstein Institute\, Golm)
DTSTART;VALUE=DATE-TIME:20210428T093000Z
DTEND;VALUE=DATE-TIME:20210428T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/32
DESCRIPTION:Title: Hertz potentials and the decay of higher-spin fields\n
by Jérémie Joudioux (Albert Einstein Institute\, Golm) as part of Prague
-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and sta
tistics\n\n\nAbstract\nThe purpose of the talk is to illustrate how differ
ential complexes can be used in relativity. Electromagnetism and linearize
d gravity (more generally higher-spin fields) are governed by hyperbolic s
ystems of partial differential equations. Solutions to these systems can b
e generated by the mean of potentials (here\, Hertz potentials) satisfying
a wave equation. It is possible to recast the problem of representing a s
olution to these higher-spin fields by Hertz potentials in the context of
the initial value problem. Initial data for higher-spin fields satisfy con
straint equations\, and cannot be chosen freely. The integrability conditi
ons for these constraints are described by elliptic complexes. These ellip
tic complexes also happen to be those describing the relation between init
ial data for higher-spin fields and those for their Hertz potentials. The
problem of describing the asymptotic behavior of generic solutions to high
er-spin fields can then be completely deduced from the asymptotic behavior
of solutions to the scalar wave equations on flat spacetime.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Van Le (Institute of Mathematics of the Czech Academy of Scie
nces)
DTSTART;VALUE=DATE-TIME:20210310T103000Z
DTEND;VALUE=DATE-TIME:20210310T113000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/33
DESCRIPTION:Title: Diffeological statistical models and diffeological Hausdor
ff measures\nby Hong Van Le (Institute of Mathematics of the Czech Aca
demy of Sciences) as part of Prague-Hradec Kralove seminar Cohomology in a
lgebra\, geometry\, physics and statistics\n\n\nAbstract\nIn my talk I sh
all first explain the concept of diffeological spaces introduced
by Souriau. Then I shall explain how to use this concept to en
dow natural smooth structures on subsets of probability measures on an
arbitrary measurable space. I shall discuss the concept of the d
iffeological Fisher metric and the resulting notion of the diffeologica
l Hausdorff measure that are categorically natural\, and meaningful
for statistical estimations used in statistical physics and data anal
ysis.\n \n My talk is based on my paper and my joi
nt paper with Alexei Tuzhilin.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Pierre Francoise (Sorbonne Université\, Paris)
DTSTART;VALUE=DATE-TIME:20210505T093000Z
DTEND;VALUE=DATE-TIME:20210505T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/34
DESCRIPTION:Title: Information Geometry and Hamiltonian Systems on Lie Groups
\nby Jean-Pierre Francoise (Sorbonne Université\, Paris) as part of P
rague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics an
d statistics\n\n\nAbstract\nThe link between Hamiltonian Integrable System
s and Information Geometry was discovered by Amari\, Fujiwara and Nakamura
(90s). In particular\, Nakamura succeeded to define the tau-function for
the open Toda Lattice by using Information Geometry .\n\nWe propose a more
general study of Hamiltonian Systems related with the Information Geometr
y on Lie groups.\n\nFisher-Rao semi-definite metric is naturally induced a
s a left-invariant semi-definite metric on the Lie group\, which is regard
ed as the parameter space of the family of probability density functions.
For a specific choice of family of probability density functions on compac
t semi-simple Lie group\, the equation for the geodesic flow is derived th
rough the Euler-Poincaré reduction. Certain perspectives are mentioned ab
out the geodesics equation on the basis of its similarity with the Bloch-B
rockett –Ratiu double bracket equation and with the Euler-Arnol'd equati
on for a generalized free rigid body dynamics.\n\nThis is a joint work wit
h Daisuke Tarama (Ritsumeikan University).\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Santi (UiT The Artic University of Norway)
DTSTART;VALUE=DATE-TIME:20210512T093000Z
DTEND;VALUE=DATE-TIME:20210512T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/35
DESCRIPTION:Title: $G(3)$ supergeometry and a supersymmetric extension of the
Hilbert-Cartan equation\nby Andrea Santi (UiT The Artic University of
Norway) as part of Prague-Hradec Kralove seminar Cohomology in algebra\,
geometry\, physics and statistics\n\n\nAbstract\nI will report on the real
ization of the simple Lie superalgebra $G(3)$ as supersymmetry of various
geometric structures – most importantly super-versions of the Hilbert–
Cartan equation and Cartan’s involutive PDE system that exhibit $G(2)$ s
ymmetry – and compute\, via Spencer cohomology groups\, the Tanaka-Weisf
eiler prolongation of the negatively graded Lie superalgebras associated w
ith two particular choices of parabolics. I will then discuss non-holonomi
c superdistributions with growth vector $(2|4\, 1|2\, 2|0)$ obtained as su
per-deformations of rank 2 distributions in a 5-dimensional space\, and sh
ow that the second Spencer cohomology group gives a binary quadric\, there
by providing a “square-root” of Cartan’s classical binary quartic in
variant for $(2\, 3\, 5)$-distributions. If time allows\, I will outline a
n extension of Tanaka’s geometric prolongation scheme to the case of sup
ermanifolds. This is a joint work with B. Kruglikov and D. The.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kotaro Kawai (Gakushuin University\, Tokyo)
DTSTART;VALUE=DATE-TIME:20210519T093000Z
DTEND;VALUE=DATE-TIME:20210519T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/36
DESCRIPTION:Title: Deformed Donaldson-Thomas connections\nby Kotaro Kawai
(Gakushuin University\, Tokyo) as part of Prague-Hradec Kralove seminar C
ohomology in algebra\, geometry\, physics and statistics\n\n\nAbstract\nTh
e deformed Donaldson-Thomas (dDT) connection is a Hermitian connection of
a Hermitian line bundle over a $G_2$-manifold satisfying certain nonlinear
PDEs. This is considered to be the mirror of a calibrated (associative) s
ubmanifold via mirror symmetry. As the name indicates\, the dDT connection
can also be considered as an analogue of the Donaldson-Thomas connection
($G_2$-instanton).\n\nIn this talk\, after reviewing these backgrounds\, I
will show that dDT connections indeed have properties similar to associat
ive submanifolds and $G_2$-instantons. I would also like to present some r
elated problems. This is joint work with Hikaru Yamamoto.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petr Zima (Charles University)
DTSTART;VALUE=DATE-TIME:20210526T093000Z
DTEND;VALUE=DATE-TIME:20210526T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/37
DESCRIPTION:Title: Symmetry\, holonomy and special geometries\nby Petr Zi
ma (Charles University) as part of Prague-Hradec Kralove seminar Cohomolog
y in algebra\, geometry\, physics and statistics\n\n\nAbstract\nVarious ty
pes of geometrical structures can be described via their so called structu
re group. This becomes especially apparent when studying homogeneous space
s. Those spaces are of the form G/H where G is a transitive symmetry group
and H is the isotropy subgroup which plays the role of structure group. A
natural question is to ask whether we can enlarge or reduce the structure
group while preserving the geometrical structure. Particular answer is gi
ven by the notion of holonomy that provides the smallest possible structur
e group H. We will review these notions and demonstrate them by examples o
f special Riemannian geometries.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jules Martel-Tordjman (University of Burgundy)
DTSTART;VALUE=DATE-TIME:20211006T093000Z
DTEND;VALUE=DATE-TIME:20211006T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/38
DESCRIPTION:Title: Modules of quantized Lie algebras and their braiding from
homology of configuration spaces\nby Jules Martel-Tordjman (University
of Burgundy) as part of Prague-Hradec Kralove seminar Cohomology in algeb
ra\, geometry\, physics and statistics\n\n\nAbstract\nFrom any semi-simple
Lie algebra\, Drinfel'd has defined an associated quantized version calle
d a quantum group. The theory of modules over quantum groups has been wide
ly used to produce topological invariants in low dimension such as: braid
groups representations\, the famous Jones polynomial for knots or topologi
cal quantum field theories à la Witten--Reshetikhin--Turaev (providing re
presentations of mapping class groups of surfaces expected to have rich pr
operties and 3-manifold invariants).\nAll these constructions rely on the
algebraic background surrounding quantum groups so that their topological
content is often mysterious in the end\, and finally the subject of many c
onjectures in this field called quantum topology.\nWe are able to recover
quantum groups modules from homology of configuration spaces\, and it give
s a homological model for quantum braid group representations and knot inv
ariants such as the ones arising from the Jones family.\n\nIn this talk I'
ll present in details how to recover the sl_2 case: quantum Verma modules
and their braiding\, from homology of configuration spaces.\nIf I have tim
e I'll say a few words on how to generalize this to every semi-simple Lie
algebra (which is a joint work in progress with S. Bigelow)\, and how it s
heds light on the topological content of Jones invariants of knots.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Borovoi (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20211013T093000Z
DTEND;VALUE=DATE-TIME:20211013T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/39
DESCRIPTION:Title: Using second Galois cohomology to search for a real point
in a real homogeneous space\nby Mikhail Borovoi (Tel Aviv University)
as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\
, physics and statistics\n\n\nAbstract\nLet G be a real algebraic group an
d Y be its real homogeneous space\, say an orbit of the complex group G(C)
\, stable under the complex conjugation\, in a linear representation of G.
We wish to find a real point in Y or to prove that Y contains no real poi
nts. We arrived at this problem when classifying trivectors on R^9. I will
explain a method of solving it using second (nonabelian) Galois cohomolog
y.\n\nNo preliminary knowledge of Galois cohomology (first or second\, abe
lian or nonabelian) is assumed.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaoru Ono (RIMS\, Kyoto)
DTSTART;VALUE=DATE-TIME:20211020T093000Z
DTEND;VALUE=DATE-TIME:20211020T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/40
DESCRIPTION:Title: An approach to the construction of virtual fundamental cyc
le/chain with integer coefficients\nby Kaoru Ono (RIMS\, Kyoto) as par
t of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, phys
ics and statistics\n\n\nAbstract\nAround 2000\, Kenji Fukaya and I propose
d the construction of \nvirtual fundamental cycle/chais with integer coeff
ients under the condition that \nthe moduli spaces carry consistent (rela
tive) stable complex structures. Starting with\nthe construction of virtu
al fundamental cycle/chains with rational coefficents\, \nI will explain o
ur ideas for the construction with integer coefficients.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Pierre Magnot (University d'Angers\, France)
DTSTART;VALUE=DATE-TIME:20211027T093000Z
DTEND;VALUE=DATE-TIME:20211027T103000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/41
DESCRIPTION:Title: On the differential geometry of groups of diffeomorphisms
and of non-formal pseudo-differential operators\nby Jean-Pierre Magnot
(University d'Angers\, France) as part of Prague-Hradec Kralove seminar C
ohomology in algebra\, geometry\, physics and statistics\n\n\nAbstract\nAf
ter reviewing a class of infinite dimensional groups based on the central
extension of a group of diffeomorphisms by a group of pseudo-differential
operators (PDOs)\, I will explain:\n\n1) how the action of the group of di
ffeomorphisms generates the dressing operator of a KP hierarchy\, which is
shown to be well-posed in a class of NON FORMAL PDOs\n\n2) How renormaliz
ed traces enables to define pseudo-Riemannian metrics on some of these gro
ups of PDOs\, different from the classical sobolev metrics present in the
literature\n\n3) how the geodesic equation of one of these metrics admit a
n infinite number of independent integrals of the motion\n\nPart of the r
esults of this talk are obtained from works in collaboration with Enrique
G. Reyes. Arxiv identifiers of related publications/preprints are: 2104.08
159 \; 2007.00387 \; 1808.03791 and 1407.1427\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arthur J. Parzygnat (IHES\, Paris)
DTSTART;VALUE=DATE-TIME:20211103T103000Z
DTEND;VALUE=DATE-TIME:20211103T113000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/42
DESCRIPTION:Title: A categorical approach to quantum probability\nby Arth
ur J. Parzygnat (IHES\, Paris) as part of Prague-Hradec Kralove seminar Co
homology in algebra\, geometry\, physics and statistics\n\n\nAbstract\nRec
ent advances in categorical probability theory suggest ideas on how to mak
e inference in quantum mechanics. I will focus on two cases\, which are Ba
yesian updating and disintegrations. Bayesian updating can be viewed as an
algorithm for making decisions or guesses based on evidence. Disintegrati
ons are special cases and are closely related to conditional expectations
and error correction in classical and quantum computation. This will be an
introduction to the subject\, and I will give many examples.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitri Alekseevsky (Institute for Information Transmission Problem
s\, Moscow)
DTSTART;VALUE=DATE-TIME:20211110T103000Z
DTEND;VALUE=DATE-TIME:20211110T113000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/43
DESCRIPTION:Title: Shortest and straightest geodesics in sub-Riemannian geome
try\nby Dmitri Alekseevsky (Institute for Information Transmission Pro
blems\, Moscow) as part of Prague-Hradec Kralove seminar Cohomology in alg
ebra\, geometry\, physics and statistics\n\n\nAbstract\nWe present a short
introduction to sub-Riemannian geometry\, concentrating\non the various d
efinitions of sub-Riemannian geodesics and their relationships.\nE. Herz r
emark that there are two main characterisations of geodesics in\nRiemannia
n geometry: geodesics as shortest curves\, based on the Mopertrui's\nprinc
iple of least action ( variational approach ) and\ngeodesics as straightes
t curves based on d'Alembert's principle of virtual\nwork.\n\nThese lead t
o different\, but equivalent definitions of geodesics in Riemannian\ngeome
try. These definitions can be generalized to sub-Riemannian geometry\,\nbu
t they become non equivalent. We consider 3 definitions of sub-Riemannian\
ngeodesics as shortest curves (Euler-Lagrange\, Hamilton and Pontryagin)\,
\nwhich mostly used in control theory and 3 definitions of geodesics as st
raightest\ncurves (d'Alembert \, Levi-Civita-Schouten and Cartan-Tanaka-Mo
rimoto )\,\nused in nonholonomic mechanics. We discuss relationship betwee
n geodesicsof different types.\nGeneralising R. Montgomery result\, we con
sider a class of sub-Riemannian\nmetrics on the total space P of the princ
ipal bundle π : P → M = P/G\nover a Riemannian manifold M with a princi
pal connection ( the Chaplygin\nsystems)\, where shortest geodesics consis
tent with straightest geodesics. This\nis an extension of the first exampl
e by L. D. Faddeev and A.M. Vershik.\nIt gives a partial answer on their q
uestion about characterization of\nsub-Riemannian manifolds with this prop
erty.\n\nUsing the geometry of flag manifolds\, we describe some classes o
f compact\nhomogeneous sub-Riemannian manifolds ( including contact sub-Ri
emannian\nmanifolds and symmetric sub-Riemannian manifolds ) where straigh
test geodesics\ncoincides with shortest geodesics. Construction of geodesi
cs in these cases\nreduces to description of Riemannian geodesics of the R
iemannian homogeneous\nmanifold.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ha Quang Minh (RIKEN Institute\, Tokyo)
DTSTART;VALUE=DATE-TIME:20211124T103000Z
DTEND;VALUE=DATE-TIME:20211124T113000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/44
DESCRIPTION:Title: Regularized information geometric and optimal transport di
stances between covariance operators and Gaussian processes\nby Ha Qua
ng Minh (RIKEN Institute\, Tokyo) as part of Prague-Hradec Kralove seminar
Cohomology in algebra\, geometry\, physics and statistics\n\n\nAbstract\n
Information geometry (IG) and Optimal transport (OT) have been attracting
much research attention in various fields\, in particular machine learning
and statistics. In this talk\, we present results on the generalization o
f IG and OT distances for finite-dimensional Gaussian measures to the sett
ing of infinite-dimensional Gaussian measures and Gaussian processes. Our
focus is on the Entropic Regularization of the 2-Wasserstein distance and
the generalization of the Fisher-Rao distance and related quantities. In b
oth settings\, regularization leads to many desirable theoretical properti
es\, including in particular dimension-independent convergence and sample
complexity. All of the presented formulations admit closed form expression
s that can be efficiently computed and applied practically.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Kruglikov (University of Tromsø)
DTSTART;VALUE=DATE-TIME:20211201T103000Z
DTEND;VALUE=DATE-TIME:20211201T113000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/45
DESCRIPTION:Title: Relative Differential Invariants\nby Boris Kruglikov (
University of Tromsø) as part of Prague-Hradec Kralove seminar Cohomology
in algebra\, geometry\, physics and statistics\n\n\nAbstract\nRelative in
variants help to understand singularities of group actions on manifolds. T
heir weights are cocycles modulo coboundaries and thus correspond to the f
irst Gelfand-Fuks cohomology. Relative differential invariants correspond
to prolongation of the action to jet-spaces\, and are important in the equ
ivalence problem. I will discuss the weight lattice and the finiteness the
orem for relative differential invariants.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Strobl (University of Lyon)
DTSTART;VALUE=DATE-TIME:20211208T103000Z
DTEND;VALUE=DATE-TIME:20211208T113000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/46
DESCRIPTION:Title: Morita equivalence of singular Riemannian foliations and I
-Poisson geometry\nby Thomas Strobl (University of Lyon) as part of Pr
ague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and
statistics\n\n\nAbstract\nWe recall the notion of singular foliations and
show how to extend it in a compatible way to the presence of a Riemannian
metric. Morita equivalence of such structures provides an equivalence rel
ation on the geometry transverse to the leaves. Finally we extend "coisot
ropic submanifolds of a Poisson manifold" to potentially singular subspace
s\, yielding what we call an I-Poisson structure\, and use this notion to
construct an invariant of singular Riemannian foliations under the above-m
entioned Morita equivalence. \nThis is joint work in progress with Hadi Na
hari.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Chernov (Dartmouth College)
DTSTART;VALUE=DATE-TIME:20211215T103000Z
DTEND;VALUE=DATE-TIME:20211215T113000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/47
DESCRIPTION:Title: Linking: causality and black holes\; and cosmic censorship
of smooth structures\nby Vladimir Chernov (Dartmouth College) as part
of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physi
cs and statistics\n\n\nAbstract\nTwo events in a spacetime are called caus
ally related if the information can get from one event point to the other.
\n \nIn the joint works with Stefan Nemirovski we established that Legendr
ian linking of the spheres of light rays passing through the two points co
mpletely determines causality for spacetimes of dimensions greater or equa
l than 4. For the spaces times of dimension 3 causal structure is complete
ly determined by topological linking.\n \nThese results settle the conject
ures of Robert Low and of Jose Natario and Paul Todd. They also give an an
swer to the problem on the Vladimir Arnold problem list communicated by Ro
ger Penrose.\n \nWe will discuss these results and some ideas about how to
apply the link theory to the study of black holes.\n \nIf time permits we
will explain why exotic smooth structures are likely not useful in genera
l relativity\, since the natural physical assumption impose strong censors
hip on the class of possible smooth structures on a spacetime and such a s
tructure is unique and natural.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pasha Zusmanovich (University Ostrava)
DTSTART;VALUE=DATE-TIME:20220302T123000Z
DTEND;VALUE=DATE-TIME:20220302T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/49
DESCRIPTION:Title: On Lie algebras in characteristic 2\nby Pasha Zusmanov
ich (University Ostrava) as part of Prague-Hradec Kralove seminar Cohomolo
gy in algebra\, geometry\, physics and statistics\n\n\nAbstract\nI will re
port on a small progress in ongoing classification efforts of simple Lie a
lgebras in characteristic 2. The main character is a certain 15-dimensiona
l simple Lie algebra which appears as a deformation of a certain semisimpl
e Lie algebra with peculiar cohomological properties.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Zuevsky (Institute of Mathematics of the Czech Academy o
f Sciences)
DTSTART;VALUE=DATE-TIME:20220309T123000Z
DTEND;VALUE=DATE-TIME:20220309T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/50
DESCRIPTION:Title: Lie algebra of operators on moduli space of Riemann surfac
es\nby Alexander Zuevsky (Institute of Mathematics of the Czech Academ
y of Sciences) as part of Prague-Hradec Kralove seminar Cohomology in alge
bra\, geometry\, physics and statistics\n\n\nAbstract\nWe recall variation
al formulas for holomorphic elements on Riemann surfaces\nwith respect to
arbitrary local coordinates on the moduli space of complex structures.\nTh
ese formulas are written in terms of a canonical element on the moduli sp
ace\nwhich corresponds to the pairing between the space of quadratic diffe
rentials and\nthe tangent space to the moduli space. Next\, we recall the
notion of continual\nLie algebras introduced by Saveliev and Vershik and
provide several classical examples.\nWe show that canonical differential o
perators on moduli space $\\mathcal M_{n\, 3g-3}$\nof Riemann surfaces for
m a continual Lie algebra with the base field given by domains\nof points
on $\\mathcal M_{n\, 3g-3}$\, where $n$ is the number of punctured points.
\nGeneral formulation of exactly solvable models associated to continual L
ie algebras\nwill be given. As an application\, we provide explicit formul
as for solutions to solvable equations.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Van Le (Institute of Mathematics of the Czech Academy of Scie
nces)
DTSTART;VALUE=DATE-TIME:20220316T123000Z
DTEND;VALUE=DATE-TIME:20220316T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/51
DESCRIPTION:Title: CR-twistor spaces over manifolds with $G_2$ -and $Spin(7)$
-structures\nby Hong Van Le (Institute of Mathematics of the Czech Aca
demy of Sciences) as part of Prague-Hradec Kralove seminar Cohomology in a
lgebra\, geometry\, physics and statistics\n\n\nAbstract\nIn 1984 LeBrun
constructed a CR-twistor space over an arbitrary conformal Riemannian
3-manifold and proved that the CR-structure is formally integrable.
This twistor construction has been generalized by Rossi in 1985 f
or $m$-dimensional Riemannian manifolds endowed with a $(m-1)$-fold vec
tor cross product (VCP). In 2011 Verbitsky generalized LeBrun's cons
truction of twistor-spaces to $7$-manifolds endowed with a
$G$-structure. In my talk I shall explain how to unify and generalize
LeBrun's\, Rossi's and Verbitsky's construction of a CR-twistor s
pace to the case where a Riemannian manifold $(M\, g)$ has
a VCP structure. Then I shall show that the formal integrability of t
he CR-structure is expressed in terms of a torsion tensor on the tw
istor space\, which is a Grassmanian bundle over $(M\, g)$. If the VCP
structure on $(M\,g)$ is generated by a $G_2$- or $Spin(7)$-structure\,
the "vertical" component of the torsion tensor vanishes\, if and only
if $(M\, g)$ has constant curvature\, and the "horizontal" component v
anishes\, if $(M\,g)$ is a torsion-free $G_2$ or $Spin(7)$-manifo
ld. Finally I shall discuss related open problems. This is a joint work
with Domenico Fiorenza.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andras Stipsicz (Alfréd Rényi Institute of Mathematics\, Hungari
an Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20220323T123000Z
DTEND;VALUE=DATE-TIME:20220323T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/52
DESCRIPTION:Title: Four-manifolds and knots\nby Andras Stipsicz (Alfréd
Rényi Institute of Mathematics\, Hungarian Academy of Sciences) as part o
f Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics
and statistics\n\n\nAbstract\nSlice knots (which bound a disk in the four
-space) play important role both\nin knot theory and in smooth four-dimens
ional topology. I will explain some of these\ncommon points\, recall a sim
ple way to construct slice knots and focus on obstructions\nof sliceness p
rovided by knot Floer homology.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Krutov (Institute of Mathematics of the Czech Academy of Sc
iences)
DTSTART;VALUE=DATE-TIME:20220330T113000Z
DTEND;VALUE=DATE-TIME:20220330T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/53
DESCRIPTION:Title: Nondegenerate invariant symmetric bilinear forms on simple
Lie superalgebras in characteristic 2\nby Andrey Krutov (Institute of
Mathematics of the Czech Academy of Sciences) as part of Prague-Hradec Kr
alove seminar Cohomology in algebra\, geometry\, physics and statistics\n\
n\nAbstract\nAs is well-known\, the dimension of the space spanned by the
non-degenerate invariant symmetric bilinear forms (NISes) on any simple fi
nite-dimensional Lie algebra or Lie superalgebra is equal to at most 1 if
the characteristic of the algebraically closed ground field is not 2.\n\nW
e prove that in characteristic 2\, the superdimension of the space spanned
by NISes can be equal to 0\, or 1\, or 0|1\, or 1|1\; it is equal to 1|1
if and only if the Lie superalgebra is a queerification (defined in arXiv:
1407.1695) of a simple classically restricted Lie algebra with a NIS (for
examples\, mainly in characteristic distinct from 2\, see arXiv:1806.05505
).\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stepan Hudecek (Charles University)
DTSTART;VALUE=DATE-TIME:20220406T113000Z
DTEND;VALUE=DATE-TIME:20220406T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/54
DESCRIPTION:Title: Symmetry and Separation of variables\nby Stepan Hudece
k (Charles University) as part of Prague-Hradec Kralove seminar Cohomology
in algebra\, geometry\, physics and statistics\n\n\nAbstract\nWe present
a condition under which a differential operator on a two dimensional manif
old admits a so-called separated solution and the separation is non-trivia
l in a sense\, that we explain. Along the way we "develop" definitions in
order to make these propositions precise\, such as of a symmetry generatin
g an operator and of a function that does not depend on a set of variables
with respect to a coordinate chart.\n\nWe are motivated by problems in Ph
ysics\, where the separation of variables is often used\, e.g.\, in specif
ic problems of electromagnetic waves\, quantum mechanics (hydrogen atom)\,
or in general relativity. In mathematical Physics the notion of separati
on was studied in many works\, including the works of Kalnins\, Winternitz
\, Miller and Koornwinder. In a part of the Physics literature\, the notio
n of the separation is studied without giving a definition of a separated
solution.\n\nIn mathematics\, more abstract versions of the separation occ
urred in the works of Stackel\, Kostant\, and M. Eastwood. However\, as fa
r as we know\, no sufficient condition on the non-triviality of a separate
d solution occurs in any of these works.\n\nThe talk is based on a bachelo
r thesis of the speaker. Joint work with S. Krysl (Math. Inst.\, Charles U
niversity).\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Markl (Institute of Mathematics of the Czech Academy of Sci
ences)
DTSTART;VALUE=DATE-TIME:20220413T113000Z
DTEND;VALUE=DATE-TIME:20220413T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/55
DESCRIPTION:Title: Combinatorics of multilinear differential operators\, or s
till another explanation of the ubiquity of Lie and strongly homotopy Lie
algebras\nby Martin Markl (Institute of Mathematics of the Czech Acade
my of Sciences) as part of Prague-Hradec Kralove seminar Cohomology in alg
ebra\, geometry\, physics and statistics\n\n\nAbstract\nAs a motivation\,
we start with an analysis of the interplay between the classical Jacobi id
entity and differential operators\, and\ncompare it with the effect of the
associator. Moving to the `quantized' level\, we compare the nature of t
he big bracket and\nIBL(=infinitesimal Lie bialgebras)-infinity algebras w
ith Terilla's quantization of associative algebras.\nIn the second part\,
we introduce a filtration mimicking combinatorial properties of multidiffe
rential operators\, and\nthe associated notion of tight operads. We then
come back to Lie algebras and give another reason why they deserve\nto be\
, along with commutative and associative algebras\, recognized as one of t
he Three Graces.\n\nThe talk will be based on the paper "Calculus of mul
tilinear differential operators\, operator $L_\\infty$-algebras and $IBL_\
\infty$-algebras"\n of Denis Bashkirov and mine. Its preprint is available
at\nhttps://arxiv.org/abs/2108.12158\, published version at https://user
s.math.cas.cz/~markl/.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitri Leites (NYUAD and Stockholm U.)
DTSTART;VALUE=DATE-TIME:20220420T113000Z
DTEND;VALUE=DATE-TIME:20220420T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/56
DESCRIPTION:Title: Structures of G(2) type in super setting and in positive c
haracteristic\, and related curvature tensors\nby Dimitri Leites (NYUA
D and Stockholm U.) as part of Prague-Hradec Kralove seminar Cohomology in
algebra\, geometry\, physics and statistics\n\n\nAbstract\nCartan and Kil
ling described finite-dimensional simple Lie algebras (over fields of real
or complex numbers) in terms of the distributions they preserve. The tech
nique of root system and Dynkin (Coxeter) graphs was discovered several de
cades later. Two o the four series of simple infinite-dimensional Lie alge
bras of vector fields are Cartan prolongations of non-positive parts of si
mple finite-dimensional Lie algebras. For any $\\mathbb{Z}$-grading of any
simple finite-dimensional Lie algebra $\\mathfrak{g}$ (bar the two series
of examples)\, the Cartan prolongation of the non-positive part of $\\mat
hfrak{g}$ returns $\\mathfrak{g}$. This is not so for the exceptional Lie
algebra $\\mathfrak{g}_2$ in characteristic 5\, whose Cartan prolongation
is called Melikyan algebra. Recall that the Lie superalgebras appeared not
in high energy physics in 1970s\, but in topology\, and either over $\\ma
thbb{Z}$ as super Lie rings\, or over finite fields. Lately\, modular Lie
(super)algebras became of interest due to their relation to quantum groups
. I intend to tell you about two modular Lie superalgebras constructed (to
gether with S.Bouarroudj and P.Grozman) a la the Melikyan algebra. I hope
to have time to say how to compute the analogs of the curvature tensors in
presence of non-integrable distribution these algebras preserve.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enxin Wu (Shantou University\, China)
DTSTART;VALUE=DATE-TIME:20220427T113000Z
DTEND;VALUE=DATE-TIME:20220427T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/57
DESCRIPTION:Title: Smooth vector spaces\nby Enxin Wu (Shantou University\
, China) as part of Prague-Hradec Kralove seminar Cohomology in algebra\,
geometry\, physics and statistics\n\n\nAbstract\nVector spaces are fundame
ntal objects in mathematics. In practice\, \nvector spaces from functional
analysis and vector bundle theory carry smooth \ninformation. In this tal
k\, I will present a general homology theory of such vector \nspaces in th
e setting of diffeology. The connection to topological vector spaces \nand
vector bundle theory will be discussed.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Iglesias-Zemmour (The Hebrew University of Jerusalem\, Isr
ael)
DTSTART;VALUE=DATE-TIME:20220504T113000Z
DTEND;VALUE=DATE-TIME:20220504T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/58
DESCRIPTION:Title: Every symplectic manifold is a (linear) coadjoint orbit\nby Patrick Iglesias-Zemmour (The Hebrew University of Jerusalem\, Israe
l) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geomet
ry\, physics and statistics\n\n\nAbstract\nI will show that every symplect
ic manifold is a (linear) coadjoint orbit of the group of automorphisms of
the integration bundle\, independently of the group of periods of the sym
plectic form. This result generalizes the Kirilov-Kostant-Souriau theorem
when the symplectic manifold is homogeneous under the action of a Lie grou
p and the symplectic form is integral.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Willem de Graaf (University of Trento)
DTSTART;VALUE=DATE-TIME:20220511T113000Z
DTEND;VALUE=DATE-TIME:20220511T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/59
DESCRIPTION:Title: Classification of four qubit and rebit states\nby Will
em de Graaf (University of Trento) as part of Prague-Hradec Kralove semina
r Cohomology in algebra\, geometry\, physics and statistics\n\n\nAbstract\
nWe consider the problem of classifying the orbits of $SL(2\, \\mathbb{C})
^4$ on the space\n$\\mathbb{C}^2 \\otimes \\mathbb{C}^2 \\otimes \\mathbb{
C}^2 \\otimes \\mathbb{C}^2$. In quantum information theory this is known
as the\nclassification of four qubit states under SLOCC operations. We app
roach\nthe problem by constructing the representation via a symmetric pair
of max-\nimal rank. This makes it possible to apply the theory of θ-repr
esentations\ndeveloped by Vinberg in the 70’s. The orbits are devided in
to three types:\nnilpotent\, semisimple and mixed. The orbits of each type
are classified sep-\narately. We also obtain the stabilizers of represent
atives of the orbits. The\ntalk will end with some comments on the same pr
oblem over R\, known as\nthe classification of four rebit states. This is
joint work with Heiko Dietrich\,\nAlessio Marrani and Marcos Origlia.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Golovko (Charles University)
DTSTART;VALUE=DATE-TIME:20221012T113000Z
DTEND;VALUE=DATE-TIME:20221012T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/60
DESCRIPTION:Title: On non-geometric augmentations in high dimensions and tors
ion of Legendrian contact homology\nby Roman Golovko (Charles Universi
ty) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geome
try\, physics and statistics\n\n\nAbstract\nWe construct the augmentations
of high dimensional Legendrian submanifolds of the contact Euclidean vect
or space which are not induced by exact Lagrangian fillings. Besides that\
, for an arbitrary finitely generated abelian group G\, we construct the e
xamples of Legendrian submanifolds whose integral linearized Legendrian c
ontact (co)homology realizes G.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Van Le (Institute of Mathematics of the Czech Academy of Scie
nces)
DTSTART;VALUE=DATE-TIME:20221019T113000Z
DTEND;VALUE=DATE-TIME:20221019T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/61
DESCRIPTION:Title: Floer-Novikov (co)homology associated with non-abelian cov
erings and symplectic fixed points\nby Hong Van Le (Institute of Mathe
matics of the Czech Academy of Sciences) as part of Prague-Hradec Kralove
seminar Cohomology in algebra\, geometry\, physics and statistics\n\n\nAbs
tract\nIn my talk I shall explain our with Kaoru Ono construction
of Floer-Novikov cohomology groups $HFN^* (M^{\\Gamma_\\xi \\times H
}\,\\xi\, Q)$ defined on a regular covering $M^{\\Gamma_\\xi \\times H}$ o
f a compact symplectic manifold $(M\, \\omega)$ with transformation
group $\\Gamma_\\xi \\times H$ and associated to a locally symple
ctic isotopy ${\\{\\varphi_t\\}}$ of $(M\, \\omega)$ with flux $\\xi \\in
H ^1 (M\, R)$. Then $H$ acts naturally on $HFN^* (M^{\\Gamma_\\xi \\time
s H}\,\\xi\, Q)$. For a subgroup $G \\subset H$ denote by $(HFN^* (M^{\
\Gamma_\\xi \\times H}\,\\xi\, Q))^G$ the subgroup of $HFN^* (M^{\\Gam
ma_\\xi \\times H}\, \\xi\, Q)$ consisting of the fixed points of the
$G$-action. We prove that the rank of $(HFN^* (M ^{\\Gamma_\\xi \\
times H}\,\\xi\, Q))^G$ equals the rank of the subgroup $(HN^*
(M^{\\Gamma_\\xi \\times H}\, Q))^G$ of the fixed points of the $G$-a
ction in the Novikov cohomology group $HN^* (M^{\\Gamma_\\xi \\times H}
\, \\Q)$. If $H$ is trivial\, this implies our previous result ass
erting that the sum of the Betti numbers of $HFN^* (M ^{\\Gamma_\\xi}
\, \\xi\, Q)$ equals the sum of the Betti numbers of the Novikov coh
omology group $HN_* (M\, \\xi\, Q)$. This equality leads to the class
ical cohomological estimate of the numbers of the fixed points of
a nondegenerate locally Hamiltonian symplectomorphism. If $H$ is nont
rivial\, we obtain a new lower bound for the number of the fixed
points of non-degenerate locally Hamiltonian symplectomorphisms of
$(M\, \\omega)$.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Pierre Magnot (University d'Angers\, France)
DTSTART;VALUE=DATE-TIME:20221026T113000Z
DTEND;VALUE=DATE-TIME:20221026T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/62
DESCRIPTION:Title: On some diffeologies on spaces of probabilities\, spaces o
f measures\, and spaces of means\nby Jean-Pierre Magnot (University d'
Angers\, France) as part of Prague-Hradec Kralove seminar Cohomology in al
gebra\, geometry\, physics and statistics\n\n\nAbstract\nPassing from prob
abilities to finite measures\, from finite measures to measures\, and from
measures to infinite dimensional integrals\,we develop examples of diffeo
logies on each of these classes of spaces\, partially from works of the au
thor\, and partially from other approaches in the existing literature. The
highlighted spaces include finite and infinite configurations\, Monte-car
lo sequences\, Radon measures\, Haar and Lebesgue integrals in the space o
f connections\, and an infinite dimensional Lebesgue mean. The highlighted
diffeologies include functional diffeology\, vague diffeology\, the Cauch
y diffeology and pro-finite diffeologies. The exposition intends to give a
rigorous differential geometric setting for some actual differential geo
metry related to probability and integration theory.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Foling Zou (University of Michigan)
DTSTART;VALUE=DATE-TIME:20221102T123000Z
DTEND;VALUE=DATE-TIME:20221102T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/63
DESCRIPTION:Title: Steenrod Algebra and Equivariant Algebraic Topology\nb
y Foling Zou (University of Michigan) as part of Prague-Hradec Kralove sem
inar Cohomology in algebra\, geometry\, physics and statistics\n\n\nAbstra
ct\nSteenrod algebra give stable cohomology operations.\nNon-equivariantly
\, the dual Steenrod algebra spectrum is a wedge of\nsuspensions of HZ/p.
It is explicitly computed and fundamental in a lot of\ncomputations in alg
ebraic topology. Consider the equivariant\nEilenberg–Maclane spectra H =
HZ/p for the cyclic group of order p. I will\ntalk about the computation
of the dual Steenrod algebra of H. It turns out\nthat when p is odd\, H
∧ H is a wedge of suspensions of H and another\nspectrum\, which we call
HM. This is joint work with Po Hu\, Igor Kriz\, and\nPetr Somberg\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenio Landi (Pennsylvania State University)
DTSTART;VALUE=DATE-TIME:20221109T123000Z
DTEND;VALUE=DATE-TIME:20221109T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/64
DESCRIPTION:Title: The Topological Half of the Grothendieck-Hirzebruch-Rieman
n-Roch Theorem\nby Eugenio Landi (Pennsylvania State University) as pa
rt of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, phy
sics and statistics\n\n\nAbstract\nThe HRR theorem famously states that th
e holomorphic Euler characteristic of $X$ with coefficients in a holomorph
ic vector bundle $V$ equals $\\int_X ch(V)td(X)$. This can be rewritten as
two theorems: the first one\, analytical\, identifying $\\chi(X\,V)$ with
the K-theoretic pushforward of $V$ to the point\, while the second\, pure
ly topological\, identifying the pushforward with the integral. The same c
an be said for the GHRR theorem and pushforwards along proper holomorphic
maps between holomorphic manifolds. I will focus on the second half\, intr
oducing orientations and pushforwards in cohomology and explaining how the
presence of the Todd class is natural and expected.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Lambie-Hanson (Institute of Mathematics of the Czech Academy
of Sciences)
DTSTART;VALUE=DATE-TIME:20221116T123000Z
DTEND;VALUE=DATE-TIME:20221116T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/65
DESCRIPTION:Title: Condensed mathematics and set theory\nby Chris Lambie-
Hanson (Institute of Mathematics of the Czech Academy of Sciences) as part
of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physi
cs and statistics\n\n\nAbstract\nRecently\, Clausen and Scholze initiated
the study of condensed mathematics\, providing a framework in which to do
algebra in situations in which the algebraic structures under consideratio
n also carry topological information. The fundamental idea is to replace t
he categories of topological spaces or topological abelian groups\, which
are poorly behaved algebraically\, with the more algebraically robust cate
gories of condensed sets or condensed abelian groups. In this talk\, we wi
ll give a very brief introduction to condensed mathematics and sketch a co
uple of very basic applications of set theoretic techniques to foundationa
l questions therein. Time permitting\, we will also briefly touch on relat
ed applications of these set theoretic ideas to other topics in homologica
l algebra.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommaso Pacini (University of Torino\, Italy)
DTSTART;VALUE=DATE-TIME:20221130T123000Z
DTEND;VALUE=DATE-TIME:20221130T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/67
DESCRIPTION:Title: G2 vs. Kähler\nby Tommaso Pacini (University of Torin
o\, Italy) as part of Prague-Hradec Kralove seminar Cohomology in algebra\
, geometry\, physics and statistics\n\n\nAbstract\nWe shall compare two ca
tegories of manifolds\, known as G2 and Kahler\, focusing on (i) their sub
manifold geometry\, (ii) their function theory. We shall also discuss inte
ractions between these topics. The talk is intended for a general audience
.\nIn particular\, we shall survey results in the preprints arXiv:2107.14117\, arXiv:2207.13956\, arXiv:2208.12535\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florio Ciaglia (Universidad Carlos III de Madrid)
DTSTART;VALUE=DATE-TIME:20221214T123000Z
DTEND;VALUE=DATE-TIME:20221214T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/68
DESCRIPTION:Title: Jordan algebras\, coadjoint orbits\, and information geome
try\nby Florio Ciaglia (Universidad Carlos III de Madrid) as part of P
rague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics an
d statistics\n\n\nAbstract\nThe purpose of this talk is to present a conne
ction between the mathematical entities mentioned in the title. It will be
argued that Jordan algebras provide a suitable playground in which parame
tric models of classical and quantum information geometry can joyfully pla
y (and hopefully thrive). In order to recover the Riemannian geometry of p
arametric models extensively used in classical and quantum information geo
metry\, the method of coadjoint orbits will be adapted to Jordan algebras.
Indeed\, given the symmetric nature of the Jordan product\, the analogue
of the Konstant-Kirillov-Souriau symplectic form becomes a symmetric covar
iant tensor field. When suitable choices of Jordan algebras are made\, it
is possible to recover the Fisher-Rao metric tensor characteristic of clas
sical information geometry or the Bures-Helstrom metric tensor appearing i
n quantum information geometry. This instance tells us that geometrical st
ructures in information geometry can be found looking at algebraic structu
res associated with Jordan algebras. The discussion will focus only on the
finite-dimensional case\, but questions and comments on the possibility o
f extending the results in infinite dimensions are welcome.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hoang Duc Luu (Max-Planck-Institute for Mathematics in Sciences\,
Leipzig)
DTSTART;VALUE=DATE-TIME:20230104T123000Z
DTEND;VALUE=DATE-TIME:20230104T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/69
DESCRIPTION:Title: Ergodicity of dynamical systems under stochastic noises\nby Hoang Duc Luu (Max-Planck-Institute for Mathematics in Sciences\, Le
ipzig) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, ge
ometry\, physics and statistics\n\n\nAbstract\nIn this talk i am going to
present how to construct and prove the ergodicity of a metric dynamical sy
stem\, from which one can generate a stochastic flow such as a random dyna
mical system. Such topic appears when one attempts to study the long term
behavior of a dynamical system under stochastic noises\, for instance stoc
hastic differential equations. We would like to consider the problem w.r.t
different types of calculus used to solve the equations\, like Ito or rou
gh path theory.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Salnikov (La Rochelle University\, France)
DTSTART;VALUE=DATE-TIME:20221207T123000Z
DTEND;VALUE=DATE-TIME:20221207T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/70
DESCRIPTION:Title: Some constructions from graded geometry\nby Vladimir S
alnikov (La Rochelle University\, France) as part of Prague-Hradec Kralove
seminar Cohomology in algebra\, geometry\, physics and statistics\n\n\nAb
stract\nIn this talk I introduce some natural constructions from the "grad
ed world"\, paying particular attention to the differences between N- and
Z- graded manifolds. I will start by the construction of the sheaf of func
tions on graded manifolds and describe its structure. The intrinsic proper
ties of this functional space are conveniently given using the language of
filtrations\, allowing to formulate the analog of Batchelor’s theorem.
Afterwards I will briefly introduce graded Hopf algebras and Harish-Chandr
a pairs\, which in turn provide the result of equivalence of categories be
tween graded Lie groups and algebras. These constructions are then used to
solve the integration problem of differential graded Lie algebras to diff
erential graded Lie groups. Time permitting\, I will also say a few words
on canonical forms of differential graded manifolds.\n\nThis talk is based
on: \n\n[1] B. Jubin\, A. Kotov\, N. Poncin\, V. Salnikov\, Differential
graded Lie groups and their differential graded Lie algebras\, Transformation Groups\, 27\, 20
22\n\n[2] A. Kotov\, V. Salnikov\, The category of Z-graded manifolds:
what happens if you do not stay positive\, Preprint: arXiv:2108.13496\n\n[3] A. Kotov\, V. Salnikov\
, Various instances of Harish-Chandra pairs\, Preprint: arXiv:2207.07083\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Misha Temkin (Dartmouth College)
DTSTART;VALUE=DATE-TIME:20230111T123000Z
DTEND;VALUE=DATE-TIME:20230111T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/72
DESCRIPTION:Title: On numbers associated with a strong Morse function\nby
Misha Temkin (Dartmouth College) as part of Prague-Hradec Kralove seminar
Cohomology in algebra\, geometry\, physics and statistics\n\n\nAbstract\n
Morse function on a manifold $M$ is called strong if all its critical poin
ts have different critical values. Given a strong Morse function $f$ and a
field $F$ we construct a bunch of elements of $F$\, which we call Bruhat
numbers (they're defined up to sign). More concretely\, Bruhat number is w
ritten on each bar in the barcode of $f$ (a.k.a. Barannikov decomposition)
. It turns out that if homology of $M$ over $F$ is that of a sphere\, then
the product of all the numbers is independent of $f$. We then construct t
he barcode and Bruhat numbers with twisted (a.k.a. local) coefficients and
prove that the mentioned product equals the Reidemeister torsion of $M$.
In particular\, it's again independent of $f$. This way we link Morse theo
ry to the Reidemeister torsion via barcodes. Time permitting\, we will als
o discuss how parametric Morse theory comes into play. Based on a joint wo
rk with Petya Pushkar\, https://arxiv.org/abs/2012.05307\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arman Taghavi-Chabert (Warsaw University)
DTSTART;VALUE=DATE-TIME:20230222T123000Z
DTEND;VALUE=DATE-TIME:20230222T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/73
DESCRIPTION:Title: Perturbations of Fefferman’s conformal structures\nb
y Arman Taghavi-Chabert (Warsaw University) as part of Prague-Hradec Kralo
ve seminar Cohomology in algebra\, geometry\, physics and statistics\n\n\n
Abstract\nIn 1976\, Charles Fefferman constructed\, in a canonical way\, a
conformal structure of Lorentzian\nsignature on a circle bundle over any
given strictly pseudo-convex Cauchy-Riemann (CR) manifolds\nof hypersurfac
e type.\n\nIt is also known\, notably through the work of Roger Penrose an
d his associates\, and of the Warsaw\ngroup led by Andrzej Trautman\, that
CR three-folds underlie four-dimensional Einstein Lorentzian\nmetrics who
se Weyl tensors are said to be algebraically special.\n\nIn this talk\, I
will show how these algebraically special Einstein metrics find a natural
formulation as exact perturbations of Fefferman’s original construction.
The additional CR data required turns out to be constrained by a non-line
ar\, or gauged\, analogue of a second-order (BGG) differential operator\,
and is related to the existence of CR functions.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hông Vân Lê (Institute of Mathematics of the Czech Academy of S
ciences)
DTSTART;VALUE=DATE-TIME:20230301T123000Z
DTEND;VALUE=DATE-TIME:20230301T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/74
DESCRIPTION:Title: Complex reflection groups and classification of $3$-forms
in $R^9$ and of $4$-forms in $R^8$\nby Hông Vân Lê (Institute of Ma
thematics of the Czech Academy of Sciences) as part of Prague-Hradec Kralo
ve seminar Cohomology in algebra\, geometry\, physics and statistics\n\n\n
Abstract\nIn my talk I shall discuss the role of complex reflection
groups in Vinberg-Elashvili's classification of 3-forms in $C^9$\,\n
Antonyan's classification of 4-forms in $C^8$ and Borovoi-De Graaf-Lê
's classification of 3-forms in $R^9$. \nI shall also explain the
role of complex reflection groups in classification of 4-forms i
n $R^8$.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petr Pushkar (Higher School of Economics\, Moscow)
DTSTART;VALUE=DATE-TIME:20230315T123000Z
DTEND;VALUE=DATE-TIME:20230315T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/75
DESCRIPTION:Title: One parameter Morse theory and Morse theory for manifolds
with boundaries\nby Petr Pushkar (Higher School of Economics\, Moscow)
as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry
\, physics and statistics\n\n\nAbstract\nLet M be a compact manifold with
boundary N and g be a generic germ of a function along N. I will explain
how one can estimate from below a number of critical points of Morse exten
sion of g to a function on M. Construction lies in one parameter Morse th
eory.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Filip Strakoš (Uppsala University)
DTSTART;VALUE=DATE-TIME:20230329T113000Z
DTEND;VALUE=DATE-TIME:20230329T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/76
DESCRIPTION:Title: Augmentations of Chekanov-Eliashberg Algebra and Geography
of Bilinearized Legendrian Contact Homology\nby Filip Strakoš (Uppsa
la University) as part of Prague-Hradec Kralove seminar Cohomology in alge
bra\, geometry\, physics and statistics\n\n\nAbstract\nWe will start with
a brief introduction to a relative version of symplectic field theory (SFT
) for Legendrian submanifolds in a particular class of contact manifolds.
This will provide us with Chekanov-Eliashberg differential graded algebra
(DGA)\, whose homology is an invariant of Legendrian isotopy. This algebra
ic structure is difficult to compute and so we will simplify the different
ial using (bi)linearization. Then we will sketch the proof of DGA-homotopy
criterion for augmentations using a duality long exact sequence\, which m
ay be seen as a version of Poincare duality for this relative SFT. We will
mention the geometric origin of those augmentations coming from exact Lag
rangian fillings of our Legendrian submanifold. If time permits\, we will
show the application of the mentioned results to the question of geography
for bilinearized Legendrian contact homology of disconnected Legendrian s
ubmanifolds in a one jet space\, which is a generalization of work of Bour
geois and Galant for the connected case.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svatopluk Krysl (Charles University)
DTSTART;VALUE=DATE-TIME:20230405T113000Z
DTEND;VALUE=DATE-TIME:20230405T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/77
DESCRIPTION:Title: Twistor complexes in symplectic geometry\nby Svatopluk
Krysl (Charles University) as part of Prague-Hradec Kralove seminar Cohom
ology in algebra\, geometry\, physics and statistics\n\n\nAbstract\nFor a
manifold with a vanishing second Stiefel--Whitney class and equipped with
a symplectic form\, it is possible to define the so-called symplectic spin
or bundle (B. Kostant) that is a parallel notion to the spinor bundle on a
Riemannian manifold. The fibre of the bundle is an infinite dimensional c
omplex vector space which is called the space of symplectic spinors. It is
a direct sum of two irreducible representations of the connected double c
over of the symplectic group.\n\n The tensor product of exterior forms on
the manifold with the symplectic spinor bundle ("twisted" deRham complex)
splits into subbundles and the symplectic twistor operators are defined wi
th help of them. We describe their construction. Computing a representatio
n-theoretic characteristic (Schur--Weyl--Howe type duality)\, we can deter
mine the symbols of the symplectic twistor operators and prove the ellipti
city of the cohomological complexes formed by these operators.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zoran Skoda (University of Zadar and University of Hradec Kralove)
DTSTART;VALUE=DATE-TIME:20230419T113000Z
DTEND;VALUE=DATE-TIME:20230419T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/78
DESCRIPTION:Title: Nonabelian Čech cocycles in noncommutative geometry\n
by Zoran Skoda (University of Zadar and University of Hradec Kralove) as p
art of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, ph
ysics and statistics\n\n\nAbstract\nGluing of sheaves\, bundles and simila
r objects is the subject of descent theory. In this talk we shall focus on
a kind of\nnoncommutative geometry where spaces are represented by Abelia
n categories which locally look like (= are glued from)\nfull categories o
f one sided modules over noncommutative "coordinate" rings. Locality may b
e in the sense\nof localizations\, but also more generally in the sense of
faithfully flat covers presented by corings.\nPrincipal bundles will have
such global spaces with categorified action analogous to a principal acti
on of a structure\ngroup and the cover of the total space will have to be
in an appropriate category respecting the action.\nA very general (nonaffi
ne) principality or Galois kind of condition will be formulated in terms o
f categorical adjunctions.\nThen the cocycles will be introduced in severa
l levels of generality\; in the main special case related to structure gro
ups\ncoming from Hopf algebras\, and locally cleft extensions\, we use com
onads in a pair of new auxiliary bicategories found in 2019.\nComparing di
fferent cocycles is first done for the case involving the same cover of th
e base.\nComparison for different base covers\, studied in a project with
M. Stojić\, uses refinements which involve additional\ndata in general. P
assing to the colimit defining cohomology classes requires some set-theore
tical care\nregarding that a priori such refinements form a proper class.\
n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Nariman (Purdue University)
DTSTART;VALUE=DATE-TIME:20230426T133000Z
DTEND;VALUE=DATE-TIME:20230426T143000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/79
DESCRIPTION:Title: On local and global invariants of flat bundles\nby Sam
Nariman (Purdue University) as part of Prague-Hradec Kralove seminar Coho
mology in algebra\, geometry\, physics and statistics\n\n\nAbstract\nChara
cteristic classes of flat bundles are related to the group cohomology of d
iffeomorphism groups. But computing the group cohomology of these large gr
oups as discrete groups is too complicated. Even calculating the second co
homology of these groups will resolve deep problems in foliation theory. H
owever\, it is easier to define certain natural cohomology classes (charac
teristic classes) in group cohomology of diffeomorphism groups. We will di
scuss that they are rarely bounded classes but some of them (e.g. Godbillo
n-Vey classes) are continuous cocycles. We will discuss some ways to detec
t their nontriviality inspired by the work of Thurston and Bott-Segal.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Nordstroem (University of Bath)
DTSTART;VALUE=DATE-TIME:20230503T113000Z
DTEND;VALUE=DATE-TIME:20230503T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/80
DESCRIPTION:Title: Massey tensors and the rational homotopy type of 7- and 8-
manifolds\nby Johannes Nordstroem (University of Bath) as part of Prag
ue-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and s
tatistics\n\n\nAbstract\nDefining tensors on the cohomology of a different
ial graded algebra by multiplying Massey products by a further element giv
es an object that has less dependence on choices than the Massey products\
, making them easier to work with. On the other hand\, all Massey products
can be recovered from these tensors when the cohomology algebra satisfies
Poincare duality\, like for the de Rham complex of a closed manifold. Mor
eover\, suitable interpretations of these tensors can capture information
about the rational homotopy type even when the Massey products are undefin
ed. For closed simply-connected 7-manifolds these tensors (along with the
cohomology algebra itself) suffice to determine the rational homotopy type
. Conjecturally the same is true for closed 8-manifolds\, but at least the
vanishing of the tensors is equivalent to formality in that case. This is
based on joint work with Diarmuid Crowley and Csaba Nagy.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Slovak (Masaryk University)
DTSTART;VALUE=DATE-TIME:20230517T113000Z
DTEND;VALUE=DATE-TIME:20230517T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/81
DESCRIPTION:Title: Almost invariant differential calculus\nby Jan Slovak
(Masaryk University) as part of Prague-Hradec Kralove seminar Cohomology i
n algebra\, geometry\, physics and statistics\n\n\nAbstract\nFor more than
hundred years\, various concepts were developed to understand the \nfield
s of geometric objects and invariant \ndifferential operators between them
for conformal Riemannian and projective geometries. More recently\, sever
al general tools were presented for the entire class of parabolic geometri
es\, i.e.\, the Cartan geometries modelled on homogeneous spaces G/P with
P a parabolic subgroup in a semi-simple Lie group G. Similarly to conforma
l Riemannian and projective structures\, all these geometries determine a
class of distinguished affine connections\, which carry an affine structur
e modelled on differential 1-forms . They correspond to reductions of P t
o its reductive Levi factor\, and they are called the Weyl structures simi
larly to the conformal case. The standard definition of differential invar
iants in this setting is as affine invariants of these connections\, which
do not depend on the choice within the class. In this talk\, we describe
a universal calculus which provides an important first step to determine s
uch invariants. I shall present a natural procedure how to construct all a
ffine invariants of Weyl connections\, which depend only tensorially on th
e deformations. This is a joint work with Andreas Cap.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Santi (University of Rome "Tor Vergata")
DTSTART;VALUE=DATE-TIME:20230510T113000Z
DTEND;VALUE=DATE-TIME:20230510T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/82
DESCRIPTION:Title: On 3-nondegenerate CR manifolds in dimension 7\nby And
rea Santi (University of Rome "Tor Vergata") as part of Prague-Hradec Kral
ove seminar Cohomology in algebra\, geometry\, physics and statistics\n\n\
nAbstract\nI will report on joint works with B. Kruglikov on CR hypersurfa
ces in C 4 with a degenerate Levi form. I will discuss the symmetry dimens
ion bound 8 for all the 3-nondegenerate 7-dimensional CR real-analytic str
uctures and present the classification of the locally homogeneous ones. Th
e bound 8 is achieved on the homogeneous model\, which is locally the only
homogeneous 3-nondegenerate 7-dimensional CR manifold.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guchuan Li (Michigan University)
DTSTART;VALUE=DATE-TIME:20230524T113000Z
DTEND;VALUE=DATE-TIME:20230524T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/83
DESCRIPTION:Title: From the real cobordism theory to the Kervaire invariant o
ne problem\nby Guchuan Li (Michigan University) as part of Prague-Hrad
ec Kralove seminar Cohomology in algebra\, geometry\, physics and statisti
cs\n\n\nAbstract\nI will review how the real cobordism theory plays an imp
ortant role in Hill—Hopkins—Ravenel’s solution to the Kervaire inva
riant one problem and leads to new computations in chromatic homotopy theo
ry at the prime 2. Then I will report about my joint work with Po Hu\, Igo
r Kriz\, Petr Somberg\, and Foling Zou on the construction of odd prime an
alogues of real cobordism theory.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Iglesias-Zemmour (The Hebrew University of Jerusalem)
DTSTART;VALUE=DATE-TIME:20230531T113000Z
DTEND;VALUE=DATE-TIME:20230531T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/84
DESCRIPTION:Title: Generalized Prequantum Bundle in Diffeology\nby Patric
k Iglesias-Zemmour (The Hebrew University of Jerusalem) as part of Prague-
Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and stat
istics\n\n\nAbstract\nI will show how we can extend the classical circle-p
requantum bundle in the case of integral symplectic manifold to any closed
2-form on any diffeological space and for any group of periods even when
the torus of period is not a circle but an irrational torus. I will discus
s the definition of the periods of the 2-form and the construction of the
generalized prequantum bundle as a quotient of the space of paths only\, w
ithout the help of an extra structure. I may give on or two singular examp
les.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Fritz (University of Innsbruck)
DTSTART;VALUE=DATE-TIME:20231004T113000Z
DTEND;VALUE=DATE-TIME:20231004T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/85
DESCRIPTION:Title: An approach to homological algebra up to $\\epsilon$\n
by Tobias Fritz (University of Innsbruck) as part of Prague-Hradec Kralove
seminar Cohomology in algebra\, geometry\, physics and statistics\n\n\nAb
stract\nA theorem of Kazhdan on approximate representations of groups is b
ased on a proof which seems to use cohomological methods "up to $\\epsilon
$". This means that being a cocycle or a coboundary is not a yes/no-proper
ty of a cochain $C$\, but rather a quantitative statement where one measur
es how strongly $C$ deviates from being either. Based on Grandis's framewo
rk for nonabelian homological algebra\, I will present a framework for suc
h quantitative homological algebra and sketch the intuition behind the res
ulting definitions of kernel and cokernel. Unfortunately\, the resulting c
ategory does not satisfy the axioms required of homological categories in
Grandis's sense. Our main result solves this problem by showing that an ar
row category is a homological category already under very weak assumptions
. It follows that derived functors and long exact sequences can be constru
cted for arrow categories quite generally\, and for quantitative homologic
al algebra in particular.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergiy Maksymenko (Institute of Mathematics NAS of Ukraine)
DTSTART;VALUE=DATE-TIME:20231011T113000Z
DTEND;VALUE=DATE-TIME:20231011T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/86
DESCRIPTION:Title: Homotopy types of diffeomorphism groups of polar Morse-Bot
t foliations on lens spaces\nby Sergiy Maksymenko (Institute of Mathem
atics NAS of Ukraine) as part of Prague-Hradec Kralove seminar Cohomology
in algebra\, geometry\, physics and statistics\n\n\nAbstract\nLet D2 = {|z
| ≤ 1} be the closed unit 2-disk in the complex plane\, and S 1 = ∂D2
be its boundary. Consider the partition F on the solid torus T = S 1 × D2
into 2-tori S 1 × {|z| = r}\, r ∈ [0\; 1]\, parallel to its boundary a
nd one singular circle S 1 × 0. A diffeomorphism h : T → T is called fo
liated (resp. leaf preserving) if for each leaf ω ∈ F its image h(ω) i
s also leaf of F (resp. h(ω) = ω). Gluing two copies of T by some diffeo
morphism between their boundaries\, one gets a lens space Lp\,q with a Mor
se-Bott foliation Fp\,q obtained from F on each copy of T. Denote by Df ol
(F\, ∂T) and Dlp(F\, ∂T) respectively the groups of foliated and leaf
preserving diffeomorphisms of T fixed on the boundary ∂T. Similarly\, le
t Df ol(Fp\,q) and Dlp(Fp\,q) be respectively the groups of foliated and l
eaf preserving diffeomorphisms of Fp\,q. Endow all those groups with the c
orresponding C ∞ Whitney topologies. The aim of the talk is to give a co
mplete description the homotopy types of the above groups Df ol(F\, ∂T)\
, Dlp(F\, ∂T)\, Df ol(Fp\,q)\, Dlp(Fp\,q) for all p\, q. In particular\,
we will show that Dlp(Fp\,q) is a strong deformation retract of Df ol(Fp\
,q). Moreover\, let D(Lp\,q) be the group of all diffeomorphisms of Lp\,q.
Then for q 6≡ 1(modp) the inclusions Isom(Lp\,q) ⊂ Dlp(Fp\,q) ⊂ Df
ol(Fp\,q) ⊂ D(Lp\,q) are weak homotopy equivalences\, where Isom(Lp\,q)
is the isometry group of Lp\,q of the canonical elliptic metric on Lp\,q.\
n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fedor Part (Institute of Mathematics\, Czech Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20231025T113000Z
DTEND;VALUE=DATE-TIME:20231025T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/87
DESCRIPTION:Title: Geometric complexity theory program and lower bounds for r
estricted models\nby Fedor Part (Institute of Mathematics\, Czech Acad
emy of Sciences) as part of Prague-Hradec Kralove seminar Cohomology in al
gebra\, geometry\, physics and statistics\n\n\nAbstract\nGeometric complex
ity theory (GCT) suggests to look on the closure of a complexity class C o
f polynomials as the closure of the orbit of a polynomial Qc under the act
ion of GL where Qc depends on C. For example\, polynomials that can be app
roximated by those computable by formulas of size S correspond to the vari
ety which is the orbit closure of the determinant of S^a x S^a matrix of v
ariables for some constant a. In the core of many complexity lower bounds
lie variations of the partial derivatives method which implicitly construc
t a polynomial F on the space of polynomials (also known as catalecticant)
such that F does not vanish on some explicit P but vanishes on all polyno
mials in a complexity class C. GCT provides a systematic program for findi
ng such separating F by studying vanishing ideals and algebras of regular
functions of orbit closure varieties using algebraic geometry and represen
tation theory. However it is not easy to implement\, despite a vast amount
of beautiful results no complexity lower bound has been proven this way s
o far. In the talk I will give an overview of the recent work relevant for
GCT approach to proving complexity lower bounds in the regime of depth 3
formulas\, which correspond to secant varieties of Chow variety\, and othe
r restricted models.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luigi Caputi (University of Turin)
DTSTART;VALUE=DATE-TIME:20231101T123000Z
DTEND;VALUE=DATE-TIME:20231101T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/88
DESCRIPTION:Title: From the Mayer-Vietoris spectral sequence to überhomology
\nby Luigi Caputi (University of Turin) as part of Prague-Hradec Kralo
ve seminar Cohomology in algebra\, geometry\, physics and statistics\n\n\n
Abstract\nÜberhomology is a recently defined triply-graded homology theor
y for simplicial complexes\, which yields both topological and combinatori
al information. When restricted to (simple) graphs\, a certain specializat
ion of überhomology yields a categorification of the connected domination
polynomial at -1\; which shows that überhomology of graphs is also relat
ed to connected dominating sets. In this talk\, after introducing the noti
on of überhomology\, and showing its relation to connected domination\, w
e shall see a further property: überhomology of simplicial complexes can
be identified with the second page of the Mayer-Vietoris spectral sequence
\, with respect to anti-star covers.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Kotrbary (Institute of Mathematics\, Charles University)
DTSTART;VALUE=DATE-TIME:20231108T123000Z
DTEND;VALUE=DATE-TIME:20231108T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/89
DESCRIPTION:Title: Towards Hodge theory for smooth translation-invariant valu
ations\nby Jan Kotrbary (Institute of Mathematics\, Charles University
) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geometr
y\, physics and statistics\n\n\nAbstract\nIt follows from seminal work of
Semyon Alesker that the space of \nsmooth\, translation-invariant valuatio
ns (finitely additive measures) \non convex bodies carries a natural struc
ture of a graded algebra \nsatisfying Poincaré duality. It is conjectured
that the Alesker \nalgebra further satisfies versions of (mixed) hard Lef
schetz theorem \nand (mixed) Hodge-Riemann relations\, i.e.\, properties f
ormally analogous \nto those of cohomology of compact Kähler manifolds. \
nIn this talk\, we will report on recent progress towards \nthis conjectur
e and explain its relevance in convex geometry\, \nin particular for geome
tric inequalities of convex bodies.\nBased on joint work with Andreas Bern
ig and Thomas Wannerer.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tornike Kadeishvili (A. Razmadze Mathematical Institute of Tbilisi
State University)
DTSTART;VALUE=DATE-TIME:20231122T123000Z
DTEND;VALUE=DATE-TIME:20231122T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/90
DESCRIPTION:Title: Homotopy algebras A(∞)\, C(∞)\, B(∞)\, hGa\nby
Tornike Kadeishvili (A. Razmadze Mathematical Institute of Tbilisi State
University) as part of Prague-Hradec Kralove seminar Cohomology in algebra
\, geometry\, physics and statistics\n\n\nAbstract\nTo construct effective
modern algebraic models now are used so called\nstrong homotopy algebras
where the classical defining identities like\n associativity\, commutativ
ity\, Jakobi\, Leibniz\, … [1] hold only up\nto coherent homotopies. We
are going to present the notions of\nhomotopy A(∞)\, C(∞)\, B(∞)\,
hGa algebras as the structures\nobtained by changing or adding some struc
tures to standard bar\nconstruction. We are going to also present some mod
els and their\napplications.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Suhr (University of Bochum)
DTSTART;VALUE=DATE-TIME:20231129T123000Z
DTEND;VALUE=DATE-TIME:20231129T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/91
DESCRIPTION:Title: The theorem of Lusternik and Schnirelmann for reversible F
insler metrics\nby Stefan Suhr (University of Bochum) as part of Pragu
e-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and st
atistics\n\n\nAbstract\nThe theorem on the existence of three simple close
d geodesics on every Riemannian 2-sphere has a "colorful" history and many
applications on closed geodesics. I will give an introduction to the prob
lem and outline a proof for the reversible Finsler case. Finally I will co
mment on some applications for closed geodesics. The talk is based on a co
llaboration with De Philippis\, Marini\, and Mazzucchelli.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfonso García-Parrado (University of Cordoba\, Spain)
DTSTART;VALUE=DATE-TIME:20231213T130000Z
DTEND;VALUE=DATE-TIME:20231213T140000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/92
DESCRIPTION:Title: An IDEAL covariant characterization of the Kerr conformal
structure\nby Alfonso García-Parrado (University of Cordoba\, Spain)
as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\
, physics and statistics\n\n\nAbstract\nWe present an **IDEAL characteriz
ation** of the family of four dimensional Lorentzian spacetimes that are
conformally related to the Kerr vacuum solution.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Druzhkov (Russian-Armenian University\, Yerevan)
DTSTART;VALUE=DATE-TIME:20231115T123000Z
DTEND;VALUE=DATE-TIME:20231115T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/93
DESCRIPTION:Title: Internal Lagrangians of PDEs\nby Konstantin Druzhkov (
Russian-Armenian University\, Yerevan) as part of Prague-Hradec Kralove se
minar Cohomology in algebra\, geometry\, physics and statistics\n\n\nAbstr
act\nIt is known that differential equations arising from the principle of
stationary action encode the variational nature in terms of their intrins
ic geometry. Three reasonable questions come up:\n\n1. Where exactly does
a variational equation contain information about its variational nature?\n
\n2. What is the meaning of cohomology that encodes the variational nature
of an equation?\n\n3. What details about the variational nature of a diff
erential equation are known to its intrinsic geometry?\n\nWe propose (part
ial) answers to these questions:\n\n1. There is a natural complex on a dif
ferential equation: quotient of the de Rham complex by the complex of twic
e Cartan forms. One of its cohomology groups encodes the variational natur
e. We call elements of this group internal Lagrangians.\n\n2. Internal Lag
rangians are related to integral functionals defined on a certain class of
submanifolds of a differential equation. Such submanifolds can be treated
as almost solutions since (informally speaking) they are composed of init
ial-boundary conditions lifted to infinitely prolonged equations.\n\nSo\,
we can introduce the notion of stationary points of an internal Lagrangian
.\n\n3. The non-degeneracy of a variational principle is inherited by the
corresponding internal Lagrangian. The case of degenerate Lagrangians requ
ires a separate study.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Van Le (Institute of Mathematics of ASCR)
DTSTART;VALUE=DATE-TIME:20231206T123000Z
DTEND;VALUE=DATE-TIME:20231206T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/94
DESCRIPTION:Title: Unital $C_\\infty$-algebras and the real homotopy type of
simply connected compact 8-manifolds\nby Hong Van Le (Institute of Mat
hematics of ASCR) as part of Prague-Hradec Kralove seminar Cohomology in a
lgebra\, geometry\, physics and statistics\n\n\nAbstract\nIn 1979 Miller s
howed that any (r-1)-connected compact manifold of dimension less than or
equal to (4r-2)\, r ≥ 2\, is formal. In 2020 Crowley-Nordström showed
that the rational homotopy type of a (r-1)-connected compact manifold $M$
of dimension less than or equal (5r-3)\, r ≥ 2\, is determined by its co
homology algebra H*(M\, Q) and by the Bianchi-Massey tensor introduced by
them. In my talk I shall explain how to encode the real homotopy type of a
(r-1)-connected compact manifold of dimension n ≤ 6r-4\, r ≥ 2\, in t
erms of a minimal unital C_∞-algebra whose higher multiplications μ_k v
anish for k ≥ 5. I shall discuss consequences and the relationship b
etween our results and several previous results on formality and homotop
y type of manifolds of low dimensions. My talk shall be based on my joint
work with Domenico Fiorenza arX
iv:2310.19506.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artem Pulemotov (University of Queensland)
DTSTART;VALUE=DATE-TIME:20240214T123000Z
DTEND;VALUE=DATE-TIME:20240214T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/95
DESCRIPTION:Title: Palais--Smale sequences for the prescribed Ricci curvature
functional\nby Artem Pulemotov (University of Queensland) as part of
Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics a
nd statistics\n\n\nAbstract\nOn homogeneous spaces\, solutions to the pres
cribed Ricci curvature equation coincide with the critical points of the s
calar curvature functional subject to a constraint. We provide a complete
description of Palais--Smale sequences for this functional. As an applicat
ion\, we obtain new existence results for the prescribed Ricci curvature e
quation\, which enables us to observe previously unseen phenomena. Joint w
ork with Wolfgang Ziller (University of Pennsylvania).\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Kotov (Hradec-Kralove University)
DTSTART;VALUE=DATE-TIME:20240221T123000Z
DTEND;VALUE=DATE-TIME:20240221T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/96
DESCRIPTION:Title: Z-graded Q-manifolds\nby Alexei Kotov (Hradec-Kralove
University) as part of Prague-Hradec Kralove seminar Cohomology in algebra
\, geometry\, physics and statistics\n\n\nAbstract\nThe main object is a Z
-graded (super)manifold supplied with a homological degree 1 vector field.
We explain the difference between non-negative\, non-positive and general
cases. A classification in the general case is given. The talk is based u
pon a joint article with Camille Laurent-Gengoux and Vladimir Salnikov.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Zvonareva (Institute of Mathematics of ASCR)
DTSTART;VALUE=DATE-TIME:20240228T123000Z
DTEND;VALUE=DATE-TIME:20240228T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/97
DESCRIPTION:Title: Functorial approach to rank functions\nby Alexandra Zv
onareva (Institute of Mathematics of ASCR) as part of Prague-Hradec Kralov
e seminar Cohomology in algebra\, geometry\, physics and statistics\n\n\nA
bstract\nFor a skeletally small triangulated category C Chuang and Lazarev
recently introduced the notion of a rank function on C. For simplicity\,
by a rank function on C we will mean an assignment to each object of C of
a non-negative real number such that certain natural conditions hold. Such
functions are closely related to functors into simple triangulated catego
ries. On the other hand\, to each skeletally small additive category C one
can associate its abelianisation mod-C. I will discuss the connection bet
ween rank functions on C and translation-invariant additive functions on m
od-C. This connection allows to use the machinery of additive functions on
abelian categories to study rank functions on triangulated categories\, t
o classify integer rank functions in terms of certain objects and to obtai
n nice decompositions. This is based on a joint work with Teresa Conde\, M
ikhail Gorsky\, and Frederik Marks.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Chernov (Dartmouth College)
DTSTART;VALUE=DATE-TIME:20240313T140000Z
DTEND;VALUE=DATE-TIME:20240313T150000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/98
DESCRIPTION:Title: Virtual Legendrian knots and possible relations to causali
ty in Borde–Sorkin spacetimes\nby Vladimir Chernov (Dartmouth Colleg
e) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geomet
ry\, physics and statistics\n\n\nAbstract\nWe review our results with Stef
an Nemirovski on the relation\nof Legendrian linking and causal structure
in globally hyperbolic\nspacetimes. After that we discuss virtual Legendri
an knots defined as\nLegendrian knots in $ST^∗M$ studied up to isotopy a
nd modification of\n$ST^∗M$ induced by surgery on M that were introduced
by Patricia Cahn\nand Asa Levi. We formulate a few conjectures about them
and\nconjecturally relate them to causality in Borde–Sorkin spacetimes
that\nare manifolds with a Lorentz metric that is degenerate at critical\n
points of a Morse "timelike" function and that consist of globally\nhyperb
olic pieces between critical levels. We prove these conjectures\nfor 2+1 d
imensional Borde–Sorkin spacetimes.\nThe talk is based on the joint work
with Rustam Sadykov.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:K V Subrahmanyam (Chennai Mathematical Institute)
DTSTART;VALUE=DATE-TIME:20240320T123000Z
DTEND;VALUE=DATE-TIME:20240320T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/99
DESCRIPTION:Title: Stabilizer limits and Orbit closures with applications to
Geometric Complexity Theory\nby K V Subrahmanyam (Chennai Mathematical
Institute) as part of Prague-Hradec Kralove seminar Cohomology in algebra
\, geometry\, physics and statistics\n\n\nAbstract\nLet $G\\subseteq GL(X)
$ be a reductive group acting on a finite dimensional vector space $V$ ove
r $\\C$. A central problem in Geometric Complexity Theory is the study poi
nts $y\,z\\in V$ where (i) $z$ is obtained as the leading term of the acti
on of a 1-parameter subgroup $\\lambda (t)\\subseteq G$ on $y$\, and (ii)
$y$ and $z$ have large distinctive stabilizers $K\,H \\subseteq G$.\n\nWe
address the question: under what conditions can (i) and (ii) be simultaneo
usly satisfied\, i.e\, there exists a 1-PS $\\lambda \\subseteq G$ for whi
ch $z$ is observed as a limit of $y$.\n\n\nUsing $\\lambda$\, we develop a
leading term analysis which applies to $V$ as well as to ${\\mathcal G}=
Lie(G)$ the Lie algebra of $G$ and its subalgebras ${\\cal K}$ and ${\\cal
H}$\, the Lie algebras of $K$ and $H$ respectively.\n\nThrough this we co
nstruct the Lie algebra $\\hat{\\mathcal K} \\subseteq {\\mathcal H}$ whic
h connects $y$ and $z$ through their Lie algebras. Here $\\hat{\\mathcal K
}$ is the leading term Lie algebra obtained from ${\\mathcal K}$ by the ad
joint action of $\\lambda(t)$. We develop the properties of $\\hat{\\mathc
al K}$ and relate it to the action of ${\\mathcal H}$ on $\\overline{N}=V/
T_z O(z)$\, the normal slice to the orbit $O(z)$.\n\n\nWe examine the case
when a semisimple element belongs to both ${\\mathcal H}$ and ${\\mathcal
K}$. We call this a *alignment*. We describe some consequences of
alignment and relate it to existing work on lower bounds in the case of th
e determinant and permanent.\n\nWe also connect alignment to *intermedi
ate $G$-varieties* $W$ which lie between the orbit closures of $z$ and
$y$\, i.e. $\\overline{O(z)} \\subsetneq W \\subsetneq O(y)$. These have
a direct bearing on representation theoretic as well as geometric properti
es which connect $z$ and $y$.\n\n\nThis is joint work with Bharat Adsul an
d Milind Sohoni.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malkhaz Bakuradze (v. Javakhishvili Tbilisi State University\, Geo
rgia)
DTSTART;VALUE=DATE-TIME:20240410T113000Z
DTEND;VALUE=DATE-TIME:20240410T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/101
DESCRIPTION:Title: Morava K-theory rings of p-groups in transferred Chern ch
aracteristic chasses I\nby Malkhaz Bakuradze (v. Javakhishvili Tbilisi
State University\, Georgia) as part of Prague-Hradec Kralove seminar Coho
mology in algebra\, geometry\, physics and statistics\n\n\nAbstract\nThis
talk provides the explicit calculations by the author and his co-authors o
n the Honda formal group law and Morava K-theory of finite groups. Much at
tention is paid to the multiplicative structure and presentation of the ge
nerators in terms of Chern classes and their transfers. This is motivated
by the still open question whether the mod -2 Morava K-theory of any finit
e group is evenly generated by the Chen classes and their transfers. This
conjecture by Hopkins-Kuhn-Ravenel was rejected by a counterexample for p
>2 case.\n\n\nIn the first lecture we present some points characteristic o
f Morava's K-theory and formal properties of the transfer map. \n\nIn the
second lecture we will look in detail at some specific examples.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malkhaz Bakuradze (v. Javakhishvili Tbilisi State University\, Geo
rgia)
DTSTART;VALUE=DATE-TIME:20240417T113000Z
DTEND;VALUE=DATE-TIME:20240417T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/102
DESCRIPTION:Title: Morava K-theory rings of p-groups in transferred Chern ch
aracteristic classes II\nby Malkhaz Bakuradze (v. Javakhishvili Tbilis
i State University\, Georgia) as part of Prague-Hradec Kralove seminar Coh
omology in algebra\, geometry\, physics and statistics\n\n\nAbstract\nThis
talk provides the explicit calculations by the author and his co-authors
on the Honda formal group law and Morava K-theory of finite groups. Much a
ttention is paid to the multiplicative structure and presentation of the g
enerators in terms of Chern classes and their transfers. This is motivated
by the still open question whether the mod -2 Morava K-theory of any fini
te group is evenly generated by the Chen classes and their transfers. This
conjecture by Hopkins-Kuhn-Ravenel was rejected by a counterexample for
p>2 case.\n\n\nIn the first lecture we present some points characteristic
of Morava's K-theory and formal properties of the transfer map. \n\nIn the
second lecture we will look in detail at some specific examples.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aliaksandr Hancharuk (Jilin University (China))
DTSTART;VALUE=DATE-TIME:20240306T123000Z
DTEND;VALUE=DATE-TIME:20240306T133000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/103
DESCRIPTION:Title: Koszul-Tate resolutions and trees\nby Aliaksandr Hanc
haruk (Jilin University (China)) as part of Prague-Hradec Kralove seminar
Cohomology in algebra\, geometry\, physics and statistics\n\n\nAbstract\nG
iven a commutative algebra O\, a proper ideal I\, and a resolution of O/I
by projective O-modules\, we construct an explicit Koszul-Tate resolution.
We call it the arborescent Koszul-Tate resolution since it is indexed by
decorated trees. When the O-module resolution has finite length\, only fin
itely many operations are needed to construct the arborescent Koszul-Tate
resolution---this is compared with the classical Tate algorithm\, which ma
y require infinitely many such computations. Examples and applications are
discussed. This is based on a joint work with Camille Laurent-Gengoux and
Thomas Strobl.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksy Tralle (University of Warmia and Mazury)
DTSTART;VALUE=DATE-TIME:20240522T113000Z
DTEND;VALUE=DATE-TIME:20240522T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/104
DESCRIPTION:by Aleksy Tralle (University of Warmia and Mazury) as part of
Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics a
nd statistics\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Kovalev (Cambridge University)
DTSTART;VALUE=DATE-TIME:20240529T113000Z
DTEND;VALUE=DATE-TIME:20240529T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/105
DESCRIPTION:by Alexei Kovalev (Cambridge University) as part of Prague-Hra
dec Kralove seminar Cohomology in algebra\, geometry\, physics and statist
ics\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petr Čoupek (Department of Probability and Mathematical Statistic
s\, Charles University)
DTSTART;VALUE=DATE-TIME:20240515T113000Z
DTEND;VALUE=DATE-TIME:20240515T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/106
DESCRIPTION:Title: Iterated integrals and controlled ODEs\nby Petr Čoup
ek (Department of Probability and Mathematical Statistics\, Charles Univer
sity) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geo
metry\, physics and statistics\n\n\nAbstract\nThe purpose of this non-tech
nical talk is to discuss the role that\niterated integrals (an instance of
the so-called mapping space signature)\nplay in the theory of ordinary di
fferential equations (ODEs) of the form\n\n \\[ \\dot{Y}(t) = f(Y(t))\\
dot{X}(t)\\]\n\nwhere the path $X$ models the input and the path $Y$ model
s the output\nof a physical system whose dynamics is governed by a (non-li
near function)\n$f$. When $X$ is sufficiently regular (e.g.\\ Lipschitz) f
unction\, the\nsolution to the ODE can be\, roughly speaking\, found as a
limit of its\niterated integrals. Such regularity is\, however\, typically
not obtained\nif $X$ is a sample path of a stochastic process (e.g.\\ the
Wiener process)\nand $\\dot X$ models the random noise (e.g.\\ the white
noise). In the talk\,\nwe will discuss why low regularity is a problem\, w
hat can be done\, and why\nit is important to understand the algebraical a
nd analytical properties of\nthe iterated integrals (and\, more generally\
, the mapping space signature).\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Camille Laurent-Gengoux (Université de Lorraine\, IECL)
DTSTART;VALUE=DATE-TIME:20240403T113000Z
DTEND;VALUE=DATE-TIME:20240403T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/107
DESCRIPTION:Title: The neighborhood of a leaf of a singular foliation\nb
y Camille Laurent-Gengoux (Université de Lorraine\, IECL) as part of Prag
ue-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and s
tatistics\n\n\nAbstract\nNear a leaf\, regular foliations are classified b
y their monodromies. What about the singular leaves of singular foliations
? The first point is that for a singular leaf\, there is a transverse sing
ular foliation\, which is constant all along the leaf. In a previous work\
, Leonid Ryvkin and I have proven that for simply connected singular leave
s with a certain type of transverse singular foliations\, there is only on
e possiblity: the direct product. Here\, we present a complete classificat
ion at the formal level\, which is composed of two parts: a sort of monodr
omy and a finite dimensional principal bundle. We use a presentation where
Yang-Mills bundles (as introduced by Kotov and Strobl) play a central rol
e. Joint work with Simon Raphael Fischer (Taipei).\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karen Strung (Institute of Mathematics of ASCR)
DTSTART;VALUE=DATE-TIME:20240424T113000Z
DTEND;VALUE=DATE-TIME:20240424T123000Z
DTSTAMP;VALUE=DATE-TIME:20240425T134845Z
UID:PHK-cohomology-seminar/108
DESCRIPTION:Title: An introduction to the classification of C*-algebras\
nby Karen Strung (Institute of Mathematics of ASCR) as part of Prague-Hrad
ec Kralove seminar Cohomology in algebra\, geometry\, physics and statisti
cs\n\n\nAbstract\nI will give an expository talk about the C*-algebra clas
sification program. In recent years\, the following classification theorem
was established after years of work by many authors:\n\n\nTheorem: Let A
and B be simple\, separable\, nuclear C*-algebras which tracially absorb t
he Jiang-Su algebra and satisfy the UCT. Then an isomorphism of the Elliot
t Invariants of A and B can be lifted to a *-isoomorphism of A and B.\n\n\
nI will explain the terms in the theorem\, and discuss how everything fits
together.\n
LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/108/
END:VEVENT
END:VCALENDAR