 Paul Balmer
Tensor triangular geometry
 Mladen Bestvina
Bounded Cohomology via QuasiTrees
 Natalia Castellana Vila
Constructing maps from pcompleted classifying spaces
 Mark Andrea de Cataldo
The Hodge theory of character varieties
 Alexander N. Dranishnikov
On Gromov's macroscopic dimension
 Nitu Kitchloo
Real JohnsonWilson Theories
 Pascal Lambrechts
On the rational homology of spaces of smooth embeddings
 Anatoly Libgober
Applications of elliptic genus
 Piotr Nowak
Controlled coarse homology and isoperimetric inequalities
 Taras Panov
From real quadrics to polytopes via manifolds
 Jörg Schürmann
Motivic characteristic classes for singular space
 Stefan Schwede
Triangulated categories: Enhancements, rigidity and exotic models
 Andrzej Zuk
Automata groups
 Paul Balmer
Tensor triangular geometry
Tensor triangular geometry is an umbrella term to designate
geometric techniques appearing via tensor triangulated categories
in various areas of mathematics, like algebraic geometry, homotopy
theory, modular representation theory, noncommutative topology,
motivic theory, etc. I will introduce the concept of spectrum of a
tensor triangulated category and try to advertise the use of this
tool, by giving some applications as well as providing some
examples of computations.
 Mladen Bestvina
Bounded Cohomology via QuasiTrees
My plan is to
present an introduction/survey starting with definitions of
quasihomomorphisms and bounded cohomology, basic construction for
free groups due to Brooks, main theorems in the subject (Bavard,
EpsteinFujiwara, BurgerMonod) with applications to rigidity, and end
with a sketch of a recent result, joint with Bromberg and Fujiwara,
that provides proofs that H^2_b(G) is infinite dimensional in all
known and several new cases (including with twisted coefficients), by
essentially reducing the situation to the Brooks argument.
 Natalia Castellana Vila
Constructing maps from pcompleted classifying spaces
In this talk I will discuss joint works with A. Libman and L. Morales.
The main tool used to understand and classify maps between pcompleted
classifying spaces
is the existence of mod p homology decompositions of these spaces in terms
of plocal information.
Usually one starts with plocal algebraic information (subgroups and
associated orbit categories) and tries
to construct a map which realizes this data after restriction. Two
situations will be described: maps between
classifying spaces of pcompleted finite groups and maps to the pcompleted
classifying space of a unitary group.
 Mark Andrea de Cataldo
The Hodge theory of character varieties
After a brief review of the statement of the decomposition
theorem, I will discuss a geometric description of the perverse
filtration on the cohomology of algebraic varieties via the
Lefschetz hyperplane theorem (joint with L. Migliorini) and I will
discuss work in progress concerning the mixed Hodge theory of
character varieties (joint work in progress with T. Hausel and L.
Migliorini).
 Alexander N. Dranishnikov
On Gromov's macroscopic dimension
Gromov introduced the notion of macroscopic dimension dim_{mc} to study
large scale properties of universal coverings X of
manifolds M with positive scalar curvature. He proposed a conjecture that
for ndimensional manifolds M always dim_{mc}X < n1.
I plan to present partial results (joint with D. Bolotov) towards Gromov's
conjecture.

Nitu Kitchloo
Real JohnsonWilson Theories
I plan to describe the nature of a family of cohomology theories
known as real JohnsonWilson theories. They can be construted as
fixed points of the involution given by complex conjugation acting
on the standard JohnsonWilson theories. I will show how these
theories have very rich structure that can be exploited to obtain
various interesting results, including new nonimmersion results
for real projectice spaces. If time permits, I will talk about the
question of orientation for these theories, and the relation to
LubinTate spectra.
 Pascal Lambrechts
On the rational homology of spaces of smooth embeddings
This is joint work with Greg Arone, Victor Turchin, and Ismar Volic.
We consider (a variation of) the space of smooth embeddings Emb(M;R^n), of
a compact manifold M in a large euclidean space. We prove that its homology
is an invariant
of the rational homotopy type of M. A
special case of this is when M is 1dimensional in which case we get
that the homology of this embedding space is the homology of
an explicit graph complex.
The techniques are GoodwillieWeiss calculus of embeddings,
Weiss orthogonal calculus, and a relative version of Kontsevich's
formality of the little disks operad.
 Anatoly Libgober
Applications of elliptic genus
I will discuss apllications
of two variable elliptic genus to various problems related to
topology of complex manifolds which inlcude algebrogeometric
analogs of Novikov conjecture, invariants of singular real
algebraic varieties and topology of loops spaces.
 Piotr Nowak
Controlled coarse homology and isoperimetric inequalities
In this talk we will introduce a controlled homology theory for
discrete metric spaces. This homology is a quasiisometry
invariant and generalizes the uniformly finite homology of Block
and Weinberger. We will present two main results. First we will
show that a certain fundamental class vanishes in linearly
controlled homology for every infinite, finitely generated group.
This is a homological version of the classical Burnside problem in
group theory, with a positive answer. Then we characterize
vanishing of the fundamental class in our homology in terms of an
isoperimetric inequality on G and show how it is related to
amenability. As applications we characterize existence of
primitives of the volume form with prescribed growth, which
generalizes Gromov's answer to Sullivan's question. We also will
show that coarse homology classes obstruct weighted Poincare
inequalities of Li and Wang and present applications to Pontryagin
classes and distortion of diffeomorphisms.
 Taras Panov
From real quadrics to polytopes via manifolds
Manifolds obtained as complete intersections of real quadratic
hypersurfaces in a complex space have a natural torus action on
them, and are known to toric topologists as momentangle
manifolds. They correspond naturally to combinatorial simple
polytopes, and a direct passage from quadrics to polytopes
involves some nice convex geometrical reasoning. The quadratic
equations or the polytopes may be very simple, while the
corresponding momentangle manifolds usually are quite complicated
topologically. Studying their topology proves to be an interesting
and challenging problem.
 Joerg Schuermann
Motivic characteristic classes for singular spaces
The talk gives an introduction to the recent theory of motivic
characteristic classes for singular spaces using the language of
BorelMoore functors due to LevineMorel. These are universal
characteristic class transformations, which can be defined on the
relative Grothendieck group of complex algebraic varieties. The
Hirzebruch class transformation unifies the following
transformations: The Chern class of MacPherson, the Todd class of
BaumFultonMacPherson and the Lclass of CappellShaneson. The
motivic Chern class transformation is a refined Ktheoretical
version unifying corresponding transformations of
BaumFultonMacPherson and of SiegelSullivan. The motivic classes
can also be defined for mixed Hodge modules leading to
characteristic classes related to intersection cohomology.
 Stefan Schwede
Triangulated categories: Enhancements, rigidity and exotic models
The notion of a triangulated category is a conceptual language used in
several areas of pure mathematics. It has two historical origins, going back
to the 1960s. In algebraic geometry, Verdier used triangulated categories as
a convenient framework to describe duality phenomena. Around the same time,
Puppe introduced a very similar notion to extract the key formal properties
of the stable homotopy category of algebraic topology.
It was apparent from the beginning though, that in many examples of interest
the passage to the triangulated category loses information. Various concept
of "models" or "enhancements" were proposed to capture the higher order
information not seen by the triangulated category. In this talk I will
survey recent results and illustrate by examples that almost anything can
happen: interesting triangulated categories may have a unique model
(rigidity), admit "exotic" models or may not have any enhancement at all.
 Andrzej Zuk
Automata groups
The class of automata groups contains several remarkable
countable groups.
Their study has led to the solution of a number of important problems
in group theory.
Its recent applications have extended to the fields of algebra,
geometry, analysis and probability.
We will present recent developments related to amenability and growth.