******************************************************
DG, 10.40, 25.11.2016
A special seminar in honor of Prof. Oldrich Kowalski
***************************************
HA, 10.40, 27.5.2016
There is no seminar
***************************************
HA, 10.40, 20.5.2016
Lada Peksova (MFF UK), Loop homotopy algebras III.
We continue the calculations presented last time, concerning the transferred
differential on the homology. We also show the connection of the homological
perturbation lemma and physics in our formalism.
***************************************
HA, 10.40, 13.5.2016
Jan Pulmann (MFF UK), Loop homotopy algebras III.
We continue the calculations presented last time, concerning the transferred
differential on the homology. We also show the connection of the homological
perturbation lemma and physics in our formalism.
***************************************
HA, 10.40, 6.5.2016
Ján Pulmann (MFF UK): Loop homotopy algebras II
Abstract. Last time we described loop homotopy algebras as solutions of quantum master equation. This week, we use this to build a deformation retract between the symmetric functions on the original vector space of the algebra and its homology. Then, using the homological perturbation lemma, we can transfer the whole master action on this homology, getting a minimal model for the original algebra.
***************************************
HA, 10.40, 29.4.2016
There is no seminar.
***************************************
HA, 10.40, 22.4.2016
Jan Pulmann (MFF UK): Loop homotopy algebras II,
Loop homotopy Lie algebra is a generalization of homotopy Lie algebra
which appears in Zwiebach's closed string field theory. We give its definition
and describe various alternative ways of describing its structure, notably
the description as solutions of quantum master equation.
***************************************
HA, 10.40, 15.4.2016
Martin Doubek (MFF UK): Homotopy tranfer for algebras over operads, III
Continuation of the previous lectures. We explain how the homotopy
transfer results from the previous lectures by Jan Pulmann for A-infinity algebras can be
generalized to algebras over cobar construction of an operad. This includes transfer
for L-infinity algebras, which will be replaced by loop homotopy (a.k.a. quantum
L-infinity) algebras in upcoming lectures.
***************************************
HA, 10.40, 8.4.2016
Martin Doubek (MFF UK): Homotopy tranfer for algebras over operads, II
Abstract.
Continuation of the previous lecture. We explain how the homotopy
transfer results from the previous lectures by Jan Pulmann for
A-infinity algebras can be generalized to algebras over cobar
construction of an operad. This includes transfer for L-infinity
algebras, which will be replaced by loop homotopy (a.k.a. quantum
L-infinity) algebras in upcoming lectures.
***************************************
HA, 10.40, 1.4.2016
Martin Doubek (MFF UK): Homotopy transfer for algebras over operads
We explain how the homotopy transfer results from the previous lectures
by Jan Pulmann for A-infinity algebras can be generalized to algebras
over cobar construction of an operad. This includes transfer for
L-infinity algebras, which will be replaced by loop homotopy (a.k.a.
quantum L-infinity) algebras in upcoming lectures.
***************************************
HA, 10.40, 18.3.2016
Jan Pulmann (MFF UK): Batalin-Vilkovisky formalism and homotopy algebras, IV
***************************************
HA, 10.40, 11.3.2016
Jan Pulmann (MFF UK): Batalin-Vilkovisky formalism and homotopy algebras, III
Abstract: BRSTand Batalin-Vilkovisky formalism play an important role in
quantization of gauge theories. However, their relevance to various
areas of mathematics has appeared recently. We will build the necessary
background and explain their relevance to the theory of homotopy
algebras and operads. We begin by reviewing the Batalin-Vilkovisky
formalism and the master equation, from algebraic and geometric
viewpoint. Then we explain how the master equation governs various
homotopy algebras, like $L_\infty$ or $A_\infty$ algebras. These
algebras, in turn, arise naturally when using operads. Therefore, we
will see versions of the master equation coming from representations of
operads,/algebras over an operad/. This week, we take a closer look at
homotopy algebras. We review the case of Lie algebras and then
generalize, to L_\infty A_\infty algebras. Then we can define their
morphisms and minimal models. Finally, we will explain the connection of
these homotopy algebras to string field theory.
***************************************
HA, 10.40, 4.3.2016
Jan Pulmann (MFF UK): Batalin-Vilkovisky formalism and homotopy algebras, II
Abstract: BRSTand Batalin-Vilkovisky formalism play an important role
in quantization of gauge theories. However, their relevance to various
areas of mathematics has appeared recently. We will build the
necessary background and explain their relevance to the theory of
homotopy algebras and operads. We begin by reviewing the
Batalin-Vilkovisky formalism and the master equation, from algebraic
and geometric viewpoint. Then we explain how the master equation
governs various homotopy algebras, like $L_\infty$ or $A_\infty$
algebras. These algebras, in turn, arise naturally when using operads.
Therefore, we will see versions of the master equation coming from
representations of operads,/algebras over an operad/. In the second
lecture, we will look at the geometry of BV formalism. The BV
Laplacian in the context of graded manifolds is a divergence, so we
will look at the generalization of Stokes theorem. This will enable us
to see the gauge invariance as a consequence of the master equation.
***************************************
HA, 10.40, 26.2.2016
Jan Pulmann (ECI): Batalin-Vilkovisky formalism and homotopy algebras.
Abstract: BRSTand Batalin-Vilkovisky formalism play an important role in
quantization of gauge theories. However, their relevance to various
areas of mathematics has appeared recently. We will build the necessary
background and explain their relevance to the theory of homotopy
algebras and operads. We begin by reviewing the Batalin-Vilkovisky
formalism and the master equation, from algebraic and geometric
viewpoint. Then we explain how the master equation governs various
homotopy algebras, like $L_\infty$ or $A_\infty$ algebras. These
algebras, in turn, arise naturally when using operads. Therefore, we
will see versions of the master equation coming from representations of
operads,/algebras over an operad/. In the first lecture, we give an
overview and sketch the background from quantum field theory. Then we
start with BV formalism from the algebraic viewpoint: Gerstenhaber
brackets, BV algebras and master equation.
***************************************
HA, 10.40, 8.1.2015
There is no seminar (Winter school pre-meeting)
***************************************
HA, 10.40, 18.12.2015
There is no seminar
***************************************
HA, 10.40, 11.12.2015
There is seminar in Brno
***************************************
HA, 10.40, 4.12.2015
Leonid Positselski (ECI): Contramodules and contraherent cosheaves in algebra and geometry
Abstract: Contramodules are module-like algebraic structures endowed
with infinite summation operations, understood algebraically as
infinitary linear operations subject to natural axioms. Simple
counterexamples show that the contramodule infinite sum cannot be
interpreted as any kind of limit of finite partial sums. Thus
contramodules represent an approach to infinite summation entirely
different from the one commonly used in analysis. Geometrically,
contramodules are a kind of module structures over formal schemes and
ind-schemes, which are an algebro-geometric version of the
differential-geometric concept of a tubular neighborhood.
Globalizing contramodules to nonaffine varieties requires the concept
of a contraherent cosheaf, which is the dual notion to that of a
quasi-coherent sheaf. Algebraically, the definition of a contraherent
cosheaf is based on the constructions of complete cotorsion theories in
the categories of modules, originally developed in connection with the
celebrated flat cover conjecture.
***************************************
HA, 10.40, 27.11.2015
Jan Gregorovic (ECI): Homogeneous parabolic geometries
Abstract: I will review the structure and construction of homogeneous parabolic
geometries. I will show, how the existence of distinguished automorphisms influences
the structure and geometric properties of homogeneous parabolic geometries. Finally,
I will present a procedure that allows algebraically compute solutions of BGG operators
on homogeneous parabolic geometries.
***************************************
HA, 10.40, 13.11.2015
Roger Howe (Yale University): Four stages of Classical Invariant, Stage 4 Theory
***************************************
HA, 10.40, 6.11.2015
Roger Howe (Yale University): Four stages of Classical Invariant, Stage 3
Theory
***************************************
HA, 10.40, 30.11.2015
Martin Doubek (MU UK, ECI): Knots, operads and graph complexes
***************************************
HA, 10.40, 23.11.2015
No Seminar
***************************************
HA, 10.40, 13.11.2015
Roger Howe (Yale University): Four stages of Classical Invariant
Theory
***************************************
HA, 10.40, 6.11.2015
Roger Howe (Yale University): Four stages of Classical Invariant
Theory
***************************************
HA, 10.40, 16.10.2015
Roger Howe (Yale University): Four stages of Classical Invariant
Theory
***************************************
HA, 10.40, 2.10.2015
Roger Howe (Yale University): Four stages of Classical Invariant
Theory
These talks will survey progress on classical invariant theory since
Weyl’s book,
with an emphasis on more recent developments.
They will begin with a brief review of Weyl’s results, including
the notion of classical action,
and Weyl’s First Fundamental Theorem for such actions. This will be
followed by the introduction
of the Weyl algebra, and the notion of dual pair of Lie subalgebras of
the symplectic Lie algebra.
These ideas permit description of the full isotopic decomposition for
classical actions,
not just the invariants, and also give rise to decomposition of
polynomial rings into invariants
and harmonics relative to a given classical action. These phenomena
suggest the concept of stable
range: when relevant parameters are restricted appropriately, various
phenomena of interest become
more tractable. For example, in the stable range, the full polynomial
ring can be expressed as the tensor
product of the invariants and the harmonics. This is referred to as
separation of variables.Seeing classical
actions as part of a dual pair structure enables consideration of the
relationship between different actions,
and leads to the study of branching rules and to reciprocity laws. These
are formulated in terms of certain
algebras, the branching algebras. Finer investigation of these issues is
aided by ideas from commutative
algebra, especially term orders, SAGBI theory and Hibi rings. These
allow detailed description
of the rings of invariants and of harmonics, and provide a natural
generalization of Hodge’s standard
monomial theory. They also enable detailed descriptions of branching
algebras, including
a representation-theoretic approach to the Littlewood-Richardson Rule.
Finally, the extent to which separation of variable fails outside
the stable range will be considered.
This is the subject of current research*********************************
*********************************
*********************************
HA, 10.40, 29.05.2015
U. Schreiber: Higher Cartan Geometry (Theory and applications).
A description of the contents can be found on the web address
http://ncatlab.org/schreiber/show/Higher+Cartan+Geometry
*********************************
HA, 10.40, 22.05.2015
U. Schreiber: Higher Cartan Geometry (Theory and applications).
A description of the contents can be found on the web address
http://ncatlab.org/schreiber/show/Higher+Cartan+Geometry
*********************************
HA, 10.40, 15.05.2015
U. Schreiber: Higher Cartan Geometry (Theory and applications).
A description of the contents can be found on the web address
http://ncatlab.org/schreiber/show/Higher+Cartan+Geometry
*********************************
HA, 10.40, 08.05.2015
No seminar
*********************************
HA, 10.40, 01.05.2015
No seminar
*********************************
HA, 10.40, 24.04.2015
U. Schreiber: Higher Cartan Geometry (Theory and applications).
A description of the contents can be found on the web address
http://ncatlab.org/schreiber/show/Higher+Cartan+Geometry
*********************************
HA, 10.40, 17.04.2015
U. Schreiber: Higher Cartan Geometry (Theory and applications).
A description of the contents can be found on the web address
http://ncatlab.org/schreiber/show/Higher+Cartan+Geometry
*********************************
HA, 10.40, 10.04.2015
U. Schreiber: Higher Cartan Geometry (Theory and applications).
A description of the contents can be found on the web address
http://ncatlab.org/schreiber/show/Higher+Cartan+Geometry
*********************************
HA, 10.40, 3.04.2015
U. Schreiber: Higher Cartan Geometry (Theory and applications).
A description of the contents can be found on the web address
http://ncatlab.org/schreiber/show/Higher+Cartan+Geometry
*********************************
HA, 10.40, 27.03.2015
U. Schreiber: Higher Cartan Geometry (Theory and applications).
A description of the contents can be found on the web address
http://ncatlab.org/schreiber/show/Higher+Cartan+Geometry
*********************************
*********************************
HA, 10.40, 20.03.2015
U. Schreiber: Higher Cartan Geometry (Theory and applications).
A description of the contents can be found on the web address
http://ncatlab.org/schreiber/show/Higher+Cartan+Geometry
*********************************
*********************************
HA, 10.40, 13.03.2015
U. Schreiber: Higher Cartan Geometry (Theory and applications).
A description of the contents can be found on the web address
http://ncatlab.org/schreiber/show/Higher+Cartan+Geometry
*********************************
*********************************
HA, 10.40, 06.03.2015
U. Schreiber: Higher Cartan Geometry (Theory and applications).
A description of the contents can be found on the web address
http://ncatlab.org/schreiber/show/Higher+Cartan+Geometry
*********************************
*********************************
HA, 10.40, 27.02.2015
U. Schreiber: Higher Cartan Geometry (Theory and applications).
A description of the contents can be found on the web address
http://ncatlab.org/schreiber/show/Higher+Cartan+Geometry
*********************************
*********************************
HA, Tuesday, Feb 24, 14.00 !!! Exceptional day/time !!!
D. Roberts (Univ. of Adelaide): Homogeneous bundles and higher geometry
The talk will be about lifting bundles of the form G --> G/H to "String 2-bundles", i.e. to
structures involving Kac-Moody loop groups.
*********************************
HA, 10.40, 20.02.2015
U. Schreiber: Higher Cartan Geometry (Theory and applications).
A description of the contents can be found on the web address
http://ncatlab.org/schreiber/show/Higher+Cartan+Geometry
*********************************
*********************************
HA, 10.40, 16.1.2015
???
*********************************
HA, 10.40, 9.1.2015
???
*********************************
HA, 10.40, 19.12.2014
There is no seminar:
*********************************************
HA, 10-11, 12.12.2014
A. Sharapov (Tomsk State University, Russia): Characteristic classes
of Q-manifolds.
Abstract: An odd vector field $Q$ on a supermanifold$M$ is called
homological, if $Q^2=0$. The operator of Lie derivative $L_Q$ makes the algebra
of smooth tensor fields
on $M$ into a differential tensor algebra. I present a complete classification
of certain invariants of homological vector fields, called characteristic classes.
These take values in the cohomology of the operator $L_Q$ and are represented by
$Q$-invariant tensors made up of the homological vector field and
a symmetric connection on $M$ by means of the algebraic tensor operations
and covariant differentiation. Some applications to the theory of Lie
algebroids and (singular) foliations will be discussed.
11-12
S. Lyakhovich**(Tomsk State University, Russia**):**BRST cohomology and quantisation of general dynamics*
Abstract:
The talk is a review of the works on the BRST embedding and quantization of
not necessarily Lagrangian or Hamiltonian dynamics.
*********************************************
HA, 10.40, 5.12.2014
U . Schreiber (University of Nijmegen): Higher Super-WZW models
I show how cocyles on super L-infinity algebras integrate to
higher WZW gerbes for sigma models on higher (categorified)
supergroups. Examples are given by the super-p-branes with tensor
multiplet fields of an extended (categorified) brane scan. This
follows arXiv:1308.5264 .
*********************************************
HA, 10.40, 28.11.2014
M. Doubek (MFF UK), Vassiliev invariants of knots
We introduce Vassiliev invariants of knots and discuss their properties,
in particular their representability by the Kontsevich integral. We will
try to clarify relations to the multiple zeta values and Drinfeld associator.
*********************************************
HA, 10.40, 21.11.2014
MES seminar in Brno.
*********************************************
HA, 10.40, 14.11.2014
M. Doubek (MFF UK), Vassiliev invariants of knots
We introduce Vassiliev invariants of knots and discuss their properties,
in particular their representability by the Kontsevich integral. We will
try to clarify relations to the multiple zeta values and Drinfeld associator.
*********************************************
HA, 10.40, 7.11.2014
M. Doubek (MFF UK), Vassiliev invariants of knots
We introduce Vassiliev invariants of knots and discuss their properties,
in particular their representability by the Kontsevich integral. We will
try to clarify relations to the multiple zeta values and Drinfeld associator.
*********************************************
HA, 10.40, 31.10.2014
M. Doubek (MFF UK), Vassiliev invariants of knots
We introduce Vassiliev invariants of knots and discuss their properties,
in particular their representability by the Kontsevich integral. We will
try to clarify relations to the multiple zeta values and Drinfeld associator.
*********************************************
HA, 10.40, 24.10.2014
ECI seminar in Trest
********************************************
HA, 10.40, 17.10.2014
M. Doubek (MFF UK), Vassiliev invariants of knots
We introduce Vassiliev invariants of knots and discuss their properties,
in particular their representability by the Kontsevich integral. We will
try to clarify relations to the multiple zeta values and Drinfeld associator.
*********************************************
HA, 10.40, 10.10.2014
M. Doubek (MFF UK), Vassiliev invariants of knots
We introduce Vassiliev invariants of knots and discuss their properties,
in particular their representability by the Kontsevich integral. We will
try to clarify relations to the multiple zeta values and Drinfeld associator.
*********************************************
HA, 10.40, 3.10.2014
M. Doubek (MFF UK), Vassiliev invariants of knots
We introduce Vassiliev invariants of knots and discuss their properties,
in particular their representability by the Kontsevich integral. We will
try to clarify relations to the multiple zeta values and Drinfeld associator.
*********************************************
*********************************************
*********************************************
HA, 11.00, 6.6.2014
Alex Feingold (Binghamton University ): A Lightcone Embedding of the Twin Building for a Hyperbolic Kac-Moody Group *
Abstract: A twin building is a simplicial complex (with further structures) associated to a group G with a
twin BN-pair, usually constructed from the parabolic subgroups of G. A hyperbolic Kac-Moody group G
over the complex numbers is associated with a hyperbolic Kac-Moody Lie algebra g = g(A), where A is
a hyperbolic type Cartan matrix that determines g by generators and relations. The invariant symmetric
bilinear form ( , ) on the standard Cartan subalgebra h in g has signature (n-1,1) on the split real form
of h, providing a Lorentzian geometry. The usual root system data of g gives a twin BN-pair for G, and thus a
twin building. The Cartan-Chevalley involution on g gives a ``compact" real form k of g, a real Lie algebra
whose complexification is g, whose Cartan subalgebra t also has Lorentzian form ( , ), and there is also
a corresponding compact real group K. We are able to embed the twin building for G inside
the union of all ``lightcones" {x in k | (x,x) <= 0} which is in the union of all K conjugates of t.
This provides a geometrical realization of the twin building of G closely related to the structure of all
Cartan subalgebras in k, and sheds light on the geometry of the infinite dimensional groups G and K. This is
especially interesting in the case of rank 3 hyperbolic algebras whose Weyl groups are hyperbolic triangle
groups, so that the building is a union of copies of the tesselated Poincar? disk with certain boundary lines
identified. This is joint work with Lisa Carbone (Rutgers University and Walter Freyn (TU-Darmstadt).
**********************************************
HA, 11.00, 23.5.2014
I. Kriz (Ann Arbor): D-structures and derived Koszul duality for unital operad algebras
Abstract: I will discuss how to make sense of derived Koszul duality
for operad algebras with unit. I will also explain how this relates to,
and, in a sense, generalizes, derived Koszul duality for PROPs,
and how the unital case relates to ideas about Koszul duality
with curvature (including the results of a recent paper of Hirsch and
Milles). Our results were inspired by D-structures, which were introduced
in bordered Floer homology by Lipshitz, Oszvath and Thurston.
This talk is about joint work with Tyler Foster and Po Hu.
**********************************************
HA, 10.40, 16.5.2014
B. Jurco: On Chern-Simons action and the Jones polynomials
**********************************************
HA, 10.40, 8.5.2014
No seminar
**********************************************
HA, 10.40, 1.5.2014
No seminar
**********************************************
HA, 10.40, 25.4.2014
L. Krizka: KZ equation, monodromy and conformal blocks
**********************************************
HA, 10.40, 18.4.2014
No seminar
**********************************************
HA, 10.40, 11.4.2014
L. Krizka: KZ equation, monodromy and conformal blocks
**********************************************
HA, 10.40, 4.4.2014
L. Krizka: KZ equation, monodromy and conformal blocks
**********************************************
HA, 10.40, 28.3.2014
L. Krizka: KZ equation, monodromy and conformal blocks
**********************************************
HA, 10.40, 21.3.2014
L. Krizka: KZ equation, monodromy and conformal blocks
**********************************************
HA, 10.40, 14.3.2014
L. Krizka: KZ equation, monodromy and conformal blocks
**********************************************
HA, 10.40, 7.3.2014
D. Mylonas (Heriot-Watt University, Edinburgh) :
Nonassociative deformations of non-geometric fluxed backgrounds in closed string theory
Abstract:
Non-geometric fluxed backgrounds arise as consistent vacua of string
theory via T-duality transformations of conventional backgrounds endowed
with p-form fluxes. In this talk we will discuss how such backgrounds
are geometrised by the dynamics of an open membrane sigma-model embedded
in the standard Courant algebroid. The boundary of this theory is a
quasi-Poisson sigma-model in phase space twisted by an abelian gerbe in
momentum space, whose correlation functions reproduce Kontsevich's
formalism of global deformation quantization. For the case of constant
flux, we will find a closed formula for the corresponding nonassociative
star product and its associator. This quantization will then be related
to cochain twist quantization via suitable quasi-Hopf algebras of
symmetries of R-fluxed phase space. In this context we will compute the
pertinent deformed differential calculus and discuss possible
realisations of nonassociative deformations of gravity.
**********************************************
HA, 10.40, 27.2.2014
M. Doubek: Invariants of knots
**********************************************
HA, 10.40, 21.2.2014
M. Doubek: Invariants of knots
**********************************************
**********************************************
**********************************************
HA, 10.40, 10.1.2014
Winter school in Srni, 2014, preparation
**********************************************
HA, 10.40, 3.1.2014
The seminar is cancelled
**********************************************
**********************************************
HA, 10.40, 13.12.2013
B. Jurco: Invariants of knots - Yang-Baxter equation in statistical physics
**********************************************
HA, 10.40, 6.12.2013
L. Krizka: Drinfeld categories
**********************************************
HA, 10.40, 29.11.2013
R. O'Buachalla: Invariants of knots
**********************************************
HA, 10.40, 22.11.2013
R. O'Buachalla: Invariants of knots
**********************************************
HA, 10.40, 15.11.2013
R. O'Buachalla: Invariants of knots
**********************************************
HA, 10.40, 8.11.2013
R. O'Buachalla: Invariants of knots
**********************************************
HA, 10.40, 1.11.2013
M. Doubek: Invariants of knots
**********************************************
HA, 10.40, 25.10.2013
M. Doubek: Invariants of knots
**********************************************
HA, 10.40, 18.10.2013
M. Doubek: Invariants of knots
**********************************************
HA, 10.40, 4.10.2013
U. Pennig: Unit spectra of K-theory via strongly self-absorbing C*-algebras
Abstract. I will speak about an operator algebraic model for the first space of
the unit spectrum of complex topological K-theory, i.e. BGL_1(KU), and related
infinite loop spaces via bundles of stabilized strongly self-absorbing C*-algebras.
The proof that the classifying space of these bundles has the right homotopy type
is based on the I-monoid model for GL_1(KU) developed by Sagave and Schlichtkrull.
I will try to keep the material self-contained, so no prior knowledge of C*-algebras is
required to follow the talk. The results are joint work with Marius Dadarlat from Purdue.
**********************************************
**********************************************
HA, 10.40, 24.5.2013
No seminar - MES in Brno
**********************************************
HA, 10.40, 17.5.2013
No seminar
**********************************************
HA, 10.40, 10.5.2013
I. Kriz (University of Michigan): Elliptic cohomology
Abstract: I will briefly introduce the idea of elliptic
cohomology, how it is constructed and why
the topic is still alive mathematically. The last part concerns
conjectured connections with analysis and geometry
which have not been established so far, even though several
attempts have been made.
***********************************************
HA, 10.40, 3.5.2013
M. Fischmann: Conformal powers of the Dirac operator via tractors
***********************************************
HA, 10.40, 26.4.2013
M. Fischmann: Conformal powers of the Dirac operator via tractors
***********************************************
HA, 10.40, 19.4.2013
V. Soucek - Howe duality for orthosymplectic Lie superalgebras
***********************************************
HA, 10.40, 12.4.2013
D. Eelbode (Ghent University): Fueter theorem from representation point of view
***********************************************
HA, 10.40, 5.4.2013
D. Smid - Fisher decomposition for orthosymplectic Lie superalgebras
************************************************
HA, 10.40, 29.3.2013
No seminar (Eastern)
***********************************************
HA, 10.40, 22.3.2013
D. Smid - Fisher decomposition for orthosymplectic Lie superalgebras
***********************************************
HA, 10.40, 15.3.2013
D. Smid - Fisher decomposition for orthosymplectic Lie superalgebras
***********************************************
HA, 10.30, 8.3.2013
Central European seminar in Brno
***********************************************
HA, 10.30, 1.3.2013
Pavel Chalmoviansky -
"What is to be expected around a singular point of plane algebraic curve?"
Anotace:
We give an overview of several results concerning singularities, their
visualizations and their application in modeling. We consider an
isolated singular point of complex plane algebraic curve and its
invariants such as Milnor number and the associated knot of the
singularity. Such a singularity can be resolved via sequence of blowups
or by a suitable unfolding. We give examples and visualizations of the
whole process. For a special class of curves, we characterize the
singular points at infinity. In real spaces, we consider a study of
relative position of a cone and a parabolic Bezier segment motivated by
Minkowski space. Singularities are used to determine boundary cases.
***********************************************
HA, 10.30, 22.2.2013
David M.J. Calderbank (Bath) - Kostant's theorem: a geometrical perspective.
The spectral decomposition of Kostant's laplacian may be viewed
as a computation on a homogeneous (or flat) Cartan geometry. From
this perspective, Kostant's result may be obtained using a first
order Weitzenbock formula relating the first order laplacian with
the curved Casimir operator on tractor-valued forms. The Weitzenbock
formula also applies in the curved case, adding an interesting
ingredient to the BGG calculus.
***********************************************
HA, 10.30, 11.1.2013
J. Nekovar (Paris) - Branching rules and diophantine equations
Abstract:
Modularity of elliptic curves implies that every elliptic curve E defined
over Q is parameterised, in many different ways, by modular and
Shimura curves. These curves are equipped with coherent families
of points defined over suitable (generalised) dihedral extensions of Q.
Non-triviality of the images of these points on E is governed by suitable
branching rules for groups SO(W) \subset SO(V) (dim W = 2, dim V = 3) over
local fields and adeles.
***********************************************
HA, 10.30, 4.1.2013
Seminar related to organization of WS, Srni
***********************************************
HA, 10.30, 21.12.2012
There is no seminar
***********************************************
HA, 10.30, 14.12.2012
T. Kobayashi (Univ. of Tokyo): Finite multiplicity theorems and real
spherical varieties
Abstract:
We introduced the concept of "Real Spherical Varieties" that
assure finite multiplicity property of irreducible infinite dimensional
representations on function spaces. More generally, I plan to discuss
geometric conditions that control the multiplicities of irreducible
representations of real reductive groups occurring in branching laws
(restriction) and Plancherel formulas (induction).
***********************************************
HA, 10.30, 7.12.2012
U. Pennig (University of Munster): Twisted K-theory
Abstract:
Twisted K-theory was first studied by Donovan and Karoubi, who called
it K-theory with local coefficients. The twists considered by them and
also later by Atiyah and Segal are represented by classes in the third
cohomology group of the underlying space. From the point of view of
stable homotopy theory, the classifying space of the units in the
K-theory spectrum $BGL_1(KU)$, which classifies all twists, is much
bigger than that: Its homotopy type is $BZ/2Z \times BBU_{\otimes}$.
We give an operator algebraic description of these higher twists,
which parallels the construction of the ordinary twists via bundles of
compact operators.
***********************************************
HA, 10.30, 30.11.2012
CES in Brno
***********************************************
HA, 10.30, 23.11.2012
B. Jurco: Introduction to string theory, I.
***********************************************
HA, 10.30, 16.11.2012
B. Jurco: Introduction to string theory, I.
***********************************************
HA, 10.30, 9.11.2012
B. Jurco: Introduction to string theory, I.
***********************************************
HA, 10.30, 2.11.2012
B. Jurco: Introduction to string theory, I.
This will be the first seminar of the series devoted to certain chapters
of the book by B. Zwiebach:
http://stringworld.ru/files/Zwiebach_B._A_first_course_in_string_theory_...
***********************************************
HA, 10.30, 26.10.2012
B. Jurco: Introductory seminar in string theory
*********************************
HA, 10.30, 12.10.2012
Leticia Barchini (Oklahoma State University): Geometric models for a class of
unitary representations, Lecture 2
This will be a series of three lectures on the following topic.
Lecture 2
Given an admissible irreducible (g, K)-module, a theorem of
Harish-Chandra guarantees that such module is the Harish-Chandra module
(i.e the space of K-finite vectors) of an irreducible representation of G.
Such equivalent class of G-representation is not unique. The different
equivalent classes of G-representations with equivalent Harish-Chandra
modules are called the globalizations of the (g,K)-module. There is always
a maximal and a min- imal globalization. These globalizations are
topological dual of each other. In the case of Aq(?), the maximal
globalization occurs in spaces of Dolbeault cohomology and the minimal
globalization occurs as compactly supported cohomology.
The problem of
describing the unitary gobalization of cohomologically induced modules is
open. I will survey the state of the problem, describe some of the methods
that have been used and or proposed indicating their partial successes. I
will focus on the various geometric-analytic subtletie of the problem. This
lecture will focus on the method known as "Indefinite quantization" and its
variants.
*********************************
HA, 10.30, 5.10.2012
Leticia Barchini (Oklahoma State University): Geometric models for a class of
unitary representations, Lecture 1
This will be a series of
three lectures on the following topic.
An open problem in representation
theory is to find explicit geometric models for irreducible unitary
representations of a real reductive group G. The space of equivalent
classes of unitary irreducible representations of G is in bijection with
the space of unitarizable irreducible Harish-Chandra mod- ules. In these
series of talk I will focus of those representations "attached" to elliptic
co-adjoint orbits. Their Harish-Chandra modules are the cohomolog- ically
induced modules, Aq(?). The aim is to build the unitary globalization of
Aq(?) that are, by algebraic methods, known to be unitarizable. In most
cases, the Hilbert space that exhibits the module as unitary is not known.
Lecture 1
In the first lecture I will discuss aspects of the
philosophy of the orbit method, illustrating the method when G = SL(2, R).
Next, I will review the classification of elliptic orbits and briefly
describe the algebraic construction of cohomologically induced modules.
*********************************
HA, 10.30, 20.4.2012
Z. Sir: Diskretni diferencialni geometrie, IV. cast
*********************************
HA, 10.30, 13.4.2012
Z. Sir: Diskretni diferencialni geometrie, III. cast
*********************************
HA, 10.30, 6.4.2012
There is no seminar
*********************************
HA, 10.30, 30.3.2012
Z. Sir: Diskretni diferencialni geometrie, II. cast
**********************************
HA, 10.30, 23.3.2012
Z. Sir: Diskretni diferencialni geometrie, I. cast
*********************************
HA, 10.30, 9.3.2012
MES Brno
*********************************
HA, 10.30, 2.3.2012
V. Tucek - Unitary representation with highest weights
and their cohomologies II.
*********************************
HA, 10.30, 24.2.2012
V. Tucek - Unitary representation with highest weights
and their cohomologies I.
*********************************
*********************************
HA, 10.30, 13.1.2012
There is no seminar
*********************************
HA, 10.30, 6.1.2012
WS Srni seminar
*********************************
HA, 10.30, 16.12.2011
The seminar is cancelled
*********************************
HA, 10.30, 9.12.2011
Vladimir Ezhov - Perturbed determinants and longest cycles on a graph.
*********************************
HA, 10.30, 2.12.2011
MES in Brno
*********************************
HA, 10.30, 25.11.2011
Z. Sir - Finite type geometry
*********************************
HA, 10.30, 18.11.2011
Seminar zrusen
*********************************
HA, 10.30, 11.11.2011
A. Juhl - On the structure of GJMS-operators
GJMS-operators are conformally invariant powers of the Laplacian. Their structure is very complicated and mysterious. In the lectureI will describe the origin of systems of identities involving these operators and how these lead to insight into their structure.
*********************************
HA, 10.30, 4.11.2011
T. Milev - Branching, vector partition function and all that
*********************************
HA, 10.30, 28.10.2011
October's fiest (no seminar)
*********************************
HA, 10.30, 21.10.2011
MES Telc
*********************************
HA, 10.30, 14.10.2011
P. Pandzic: Translation principle for Dirac index
Let G be a connected real reductive Lie group with maximal compact subgroup
K of equal rank and with complexified Lie algebra g. If X is a (g,K)-module,
then the Dirac cohomology of X splits into even and odd parts, and Dirac
index is defined as their formal difference. We study how Dirac index can
vary in a coherent family of (virtual) (g,K)-modules. This is joint work in
progress with Salah Mehdi and David Vogan.
*********************************
HA, 10.30, 7.10.2011
L. Schwachhoefer - Euclidean and hyperbolic monopoles.
*********************************
*********************************
HA, 10.30, 3.6.2011
T. Salac - BGG category O
*********************************
HA, 10.30, 20.5.2011
T. Salac - BGG category O
*********************************
HA, 10.30, 13.5.2011
ECC Radejov
*********************************
HA, 10.30, 6.5.2011
D. M. J. Calderbank: Parabolic subgeometries - un update.
*******************************
HA, 10.30, 29.4.2011
D. M. J. Calderbank: H-projective structures - a lost parabolic geometry?
*********************************
HA, 10.30, 22.4.2011
H. De Bie - Clifford-Fourier transform and Hermite semigroups
*********************************
HA, 10.30, 15.4.2011
B. Jurco - Hamiltonian reduction + Calogero-Moser systems
*********************************
HA, 10.30, 8.4.2011
T. Salac - BGG category O
*********************************
HA, 10.30, 1.4.2011
Special seminars
*********************************
HA, 10.30, 25.3.2011
T. Salac - BGG category O
*********************************
HA, 10.30, 18.3.2011
Z. Vlasakova - Symetrie CR Laplaceova operatoru
*********************************
HA, 10.30, 11.3.2011
Z. Vlasakova - Symetrie CR Laplaceova operatoru
*********************************
HA, 10.30, 4.3.2011
MES in Brno
*********************************
HA, 10.30, 25.2.2011
T. Salac - Elliptic complexes in Clifford Analysis
*********************************
HA, 10.30, 14.1.2011
No seminar
*********************************
HA, 10.30, 7.1.2011
No seminar
*********************************
HA, 10.30, 17.12.2010
V. Soucek - Cherednik algebras and their representation theory
*********************************
HA, 10.30, 10.12.2010
V. Soucek - Cherednik algebras and their representation theory
*********************************
HA, 10.30, 3.12.2010
The seminar is cancelled
*********************************
HA, 10.30, 26.11.2010
P. Somberg - Representation theory and D-modules
*********************************
HA, 10.30, 19.11.2010
(Lecture given in Mikulov)
Lorenz Schwachhoefer - Extrinsic symmetric spaces
*********************************
*********************************
DG, 10.30, 15.10.2010
P. Somberg - Representation theory and D-modules
*********************************
DG, 10.30, 8.10.2010
P. Somberg - Representation theory and D-modules
*********************************
DG, 10.30, 1.10.2010
P. Somberg - Representation theory and D-modules
*********************************
DG, 10.30, 1.10.2010
Seminar se nekona
*********************************
*********************************
*********************************
DG, 10.30, 28.5.2010
MES in Brno
*********************************
DG, 10.30, 21.5.2010
Z. Sir - Problemy geometrickeho modelovani
*********************************
DG, 10.30, 14.5.2010
Z. Kasarova - Introduction to CR geometry
*********************************
DG, 10.30, 7.5.2010
W. Sabadani: Slice hyperholomorphic functions and the Fueter mapping
theorem in integral form
F. Colombo: Fhe functional calculi associated to slice hyperholomorphic
functions.
*********************************
DG, 10.30, 30.4.2010
MES, Brno
*********************************
DG, 10.30, 23.4.2010
Z. Kasarova - Introduction to CR geometry
*********************************
DG, 10.30, 16.4.2010
S. Krysl - Symplekticke spinory
*********************************
DG, 10.30, 9.4.2010
P. Pandzic (Zahreb University) - Dirac cohomology and generalized Bott-Borel-Weil Theorem
**********************************
DG, 10.30, 2.4.2010
The seminar is cancelled
*********************************
DG, 10.30, 26.3.2010
S. Krysl - Symplekticke spinory
**********************************
DG, 10.30, 19.3.2010
S. Krysl - Symplekticke spinory
**********************************
DG, 10.30, 12.3.2010
L. Krizka - Geometric methods in representation theory
**********************************
DG, 10.30, 5.3.2010
L. Krizka - Geometric methods in representation theory
*********************************
DG, 10.30, 26.2.2010
MES, Brno
**********************************
HA, 10.30, 15.1.2010
The seminar is cancelled
**********************************
HA, 10.30, 8.1.2010
Winter school Srni (preparation); the meeting is at 10!
**********************************
HA, 10.30, 18.12.2009
Branislav Jurco - Introduction to nonabelian bundle gerbes
**********************************
HA, 10.30, 11.12.2009
MES in Brno
**********************************
HA, 10.30, 4.12.2009
S. Krysl - Svazky a jejich kohomologie
**********************************
HA, 10.30, 27.11.2009
S. Krysl - Svazky a jejich kohomologie
**********************************
HA, 10.30, 20.11.2009
S. Krysl - Svazky a jejich kohomologie
**********************************
HA, 10.30, 13.11.2009
S. Krysl - Svazky a jejich kohomologie
**********************************
HA, 10.30, 6.11.2009
T. Salac - Dirac operators in many variables
**********************************
HA, 10.30, 30.10.2009
Seminar is cancelled
**********************************
HA, 10.30, 23.10.2009
T. Salac - Dirac operators in many variables
**********************************
HA, 10.30, 16.10.2009
Thang Le - Hyperbolic volume, torsion growth, and L2-torsion
**********************************
HA, 10.30, 9.10.2009
V. Tucek - Symetrie Laplaceova operatoru
**********************************
HA, 10.30, 2.10.2009
MES in Brno
**********************************
**********************************
**********************************
HA, 10.30, 22.5.2009
P. Franek -
**********************************
HA, 10.30, 15.5.2009
T. Salac - Explicit form of generalized Dolbeault complexes
**********************************
HA, 10.30, 17.4.2009
MES in Brno
**********************************
HA, 10.30, 10.4.2009
The seminar is cancelled
**********************************
HA, 10.30, 3.4.2009
P. Franek - Cartan for beginners
**********************************
HA, 10.30, 27.3.2009
P. Franek - Cartan for beginners
**********************************
HA, 10.30, 20.3.2009
P. Franek - Cartan for beginners
**********************************
HA, 10.30, 13.3.2009
P. Franek - Cartan for beginners
**********************************
HA, 10.30, 6.3.2009
Ren - ???
**********************************
HA, 10.30, 27.2.2009
MES, Brno
**********************************
**********************************
HA, 10.30, 16.1.2009
L. Krizka, P. Somberg - Stability in abelian categories and D-branes
**********************************
HA, 10.30, 9.1.2009
**********************************
DG, 9.00, 19.12.2008
CES, Brno
**********************************
DG, 9.00, 12.12.2008
Workshop on Clifford Analysis
**********************************
HA, 10.30, 5.12.2008
P. Franek - Cartan for beginners
**********************************
HA, 10.30, 28.11.2008
P. Franek - Cartan for beginners
**********************************
HA, 10.30, 21.11.2008
P. Franek - Cartan for beginners
**********************************
HA, 10.30, 14.11.2008
ECC seminars Friday+Saturday (Telc/Trest)
**********************************
HA, 10.30, 7.11.2008
P. Franek - Cartan for beginners
**********************************
HA, 10.30, 31.10.2008
L. Krizka, M. Sikora - Alg. Geometry, D-modules and Fourier-Mukai transform
**********************************
HA, 10.30, 24.10.2008
L. Krizka, M. Sikora - Alg. Geometry, D-modules and Fourier-Mukai transform
**********************************
HA, 10.30, 17.10.2008
V. Tucek, T. Salac - Geometry of algebraic stacks
**********************************
HA, 10.10.2008
CES, Brno
**********************************
HA, 10.30, 3.10.2008
V. Tucek, T. Salac - Geometry of algebraic stacks
**********************************
**********************************
HA, 10.30, 23.5.2008
V. Soucek - Holonomic D-modules and their applications
**********************************
HA, 10.30, 16.5.2008
V. Soucek - Holonomic D-modules and their applications
**********************************
HA, 10.30, 9.5.2008
The seminar is cancelled due to the feast
**********************************
HA, 10.30, 2.5.2008
K. Pazourek - Cayleho rovina
**********************************
HA, 10.30, 25.4.2008
S. Chiossi -
**********************************
HA, 10.30, 18.4.2008
Seminar MES in Brno
**********************************
HA, 10.30, 11.4.2008
P. Somberg - Introduction to D-modules
**********************************
HA, 10.30, 4.4.2008
No seminar
**********************************
HA, 10.30, 28.3.2008
P. Somberg - Introduction to D-modules
**********************************
HA, 10.30, 21.3.2008
Easter feast
**********************************
HA, 10.30, 14.3.2008
Seminar MES in Brno
**********************************
HA, 10.30, 7.3.2008
P. Somberg - Introduction to D-modules
**********************************
HA, 10.30, 29.2.2008
P. Somberg - Introduction to D-modules
**********************************
HA, 10.30, 22.2.2008
P. Somberg - Introduction to D-modules
**********************************
WS, Srni
**************************************
HA, 10.30, 2.10.2009
MES in Brno
HA, 10.30, 23.10.2009
?
**************************************
HA, 10.30, 16.10.2009
?
Čeština
English