dg-categories lecture II (after Toen
Derived equivalences of Hilbert schemes and generalized Kummer varieties
dg-categories lecture I (after Toen)
Descent for $n$-Bundles
We study principal bundles for strict Lie $n$-groups over simplicial manifolds. Given a Lie group $G$, one can construct a principal $G$-bundle on a manifold $M$ by taking a cover $U$ of $M$, specifying a transition cocycle, and then quotienting $U\times G$ by the equivalence relation generated by the cocycle. We demonstrate the existence of an analogous construction for arbitrary strict Lie $n$-groups. As an application, we show how our construction leads to a simple finite dimensional model of the Lie 2-group String($n$).
A differential graded approach to derived differential geometry, Part 4
Course on the theory of p-local finite groups
Morse theory for Hamiltonians
Zipf's Law and Kolmogorov complexity
Zipf's law was discovered as an empirical probability distribution
governing the frequency of usage of words in a language. Later
it was observed in many other situations. As Terence Tao recently remarked,
it still lacks a convincing and satisfactory mathematical explanation.
In this talk I suggest that at least in certain cases, Zipf's law can be explained as
a special case of the a priori distribution introduced and studied by L.~Levin.
The Zipf ranking corresponding to diminishing frequency appears then as the
ordering determined by the growing Kolmogorov complexity.
In my talk, I will explain the basics of theoretical computability theory and
the place of Kolmogorov complexity in it. Extensions of tis construction lead
to interesting new question in the theory of operads.
On an order on the set of partial flag varieties
In 1974 R.W. Richardson have constructed a map from the set of parabolic
subgroups of a given reductive group G to the set of nilpotent co-adjoint
orbits in g*. Natural inclusion-in-closure order on the set of nilpotent
co-adjoint orbits induces, via the Richardson map, a partial order on the
set of parabolic subgroups of a given reductive group G.
Classes of conjugacy of parabolic subgroups in a simple classical Lie
group can be identified with (isotropic) flag varieties. Thus Richardson
map induces a partial order on the set of (isotropic) partial flag
varieties.
In my talk I will describe this order on the set of flag varieties in
terms of Young diagrams and apply this description to a classification of
spherical actions on flag varieties (this is some class of G-actions with
finitely many G-orbits). This classification was obtained in a joint work
with R.~Avdeev and heavily depends on a recent result of I.~Losev.
4-manifolds circa 1974: surgery and h-cobordism, finding dual spheres
Sphere to sphere theorem
New guests at the MPIM
4-manifold Discussion Session
4-manifold Discussion Session
On the geometry of the Batalin-Vilkovisky Laplacian
We define a jet-space analogue of the BV-Laplacian, avoiding
delta-functions and infinite constants; instead we show that the main
properties of the BV-Laplacian, which is a necessary ingredient in the
quantisation of gauge-invariant systems of Euler-Lagrange equations, and
its relation to the Schouten bracket originate from the underlying
jet-space geometry.
On the Fourier coefficients of meromorphic Jacobi forms
It is a well known fact that a holomorphic Jacobi form $\phi$ splits into the so called theta--decomposition, and that the associated theta coefficients (essentially the Fourier coefficients of $\phi$) are modular forms. Although a similar decomposition is not possible if $\phi$ is meromorphic, in their recent paper Dabholkar, Murthy, and Zagier extended this construction providing a canonical decomposition of $\phi$, defining the so called canonical Fourier coefficients of $\phi$, and describing their modular property in the case of poles of order at most 2. In this talk we show how to extend the previous construction to the case of poles of arbitrary order, and we prove that the canonical Fourier coefficients are the holomorphic part of a certain generalization of harmonic weak Maass forms called almost harmonic weak Maass forms, a new automorphic object recently introduced by Bringmann and Folsom.
A differential graded approach to derived differential geometry, Part 3
A differential graded approach to derived differential geometry, Part 2
A differential graded approach to derived differential geometry, Part 1
Langlands correspondence II
English
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