- You are here:
- GT Home
- Home
- News & Events

Series: Geometry Topology Seminar

Series: Combinatorics Seminar

Lovasz Local Lemma (LLL) is a powerful result in probability theory that states that the probability that none of a set of bad events happens is nonzero if the probability of each event is small compared to the number of events that depend on it. It is often used in combination with the probabilistic method for non-constructive existence proofs. A prominent application of LLL is to k-CNF formulas, where LLL implies that, if every clause in the formula shares variables with at most d \le 2^k/e other clauses then such a formula has a satisfying assignment. Recently, a randomized algorithm to efficiently construct a satisfying assignment was given by Moser. Subsequently Moser and Tardos gave a randomized algorithm to construct the structures guaranteed by the LLL in a very general algorithmic framework. We will address the main problem left open by Moser and Tardos of derandomizing their algorithm efficiently when the number of other events that any bad event depends on is possibly unbounded. An interesting special case of the open problem is the k-CNF problem when k = \omega(1), that is, when k is more than a constant.

Series: SIAM Student Seminar

In this talk we will review some of the classical weighted theory for singular integral operators, and discuss some recent progress on finding sharp bounds in terms of the A_p constant associated with the weight

Series: Math Physics Seminar

The McK--V system is a non--linear diffusion equation with a non--local
non--linearity provided by convolution. Recently popular in a variety
of applications, it enjoys an ancient heritage as a basis for
understanding equilibrium and near equilibrium fluids. The model is
discussed in finite volume where, on the basis of the physical
considerations, the correct scaling (for the model itself) is
identified. For dimension two and above and in large volume, the phase
structure of the model is completely elucidated in (somewhat
disturbing) contrast to dynamical results. This seminar represents
joint work with V. Panferov.

Series: Stochastics Seminar

The goal of this talk is to present a new method for sparse estimation
which does not use standard techniques such as $\ell_1$ penalization.
First, we introduce a new setup for aggregation which bears strong links
with generalized linear models and thus encompasses various response
models such as Gaussian regression and binary classification. Second, by
combining maximum likelihood estimators using exponential weights we
derive a new procedure for sparse estimations which satisfies exact
oracle inequalities with the desired remainder term. Even though the
procedure is simple, its implementation is not straightforward but it
can be approximated using the Metropolis algorithm which results in a
stochastic greedy algorithm and performs surprisingly well in a
simulated problem of sparse recovery.

Series: Graph Theory Seminar

We will discuss the classic theorem of Walter Schnyder: a graph G is planar if and only if the dimension of its incidence poset is at most 3. This result has been extended by Brightwell and Trotter to show that the dimension of the vertex-edge-face poset of a planar 3-connected graph is 4 and the removal of any vertex (or by duality, any face) reduces the dimension to 3. Recently, this result and its extension to planar multigraphs was key to resolving the question of the dimension of the adjacency poset of a planar bipartite graph. It also serves to motivate questions about the dimension of posets with planar cover graphs.

Series: Analysis Seminar

We will survey recent developments in the area of two weight inequalities, especially those relevant for singular integrals. In the second lecture, we will go into some details of recent characterizations of maximal singular integrals of the speaker, Eric Sawyer, and Ignacio Uriate-Tuero.

Series: ACO Student Seminar

Sum-Product inequalities originated in the early 80's
with the work of Erdos and Szemeredi, who showed that there exists
a constant c such that if A is a set of n integers, n sufficiently
large, then either the sumset A+A = {a+b : a,b in A} or the product
set A.A = {ab : a,b in A}, must exceed n^(1+c) in size. Since that
time the subject has exploded with a vast number of generalizations
and extensions of the basic result, which has led to many
very interesting unsolved problems (that would make great thesis
topics). In this talk I will survey some of the developments in this
fast-growing area.

Series: Other Talks

In these talks we will introduced the basic definitions and examples of presheaves, sheaves and sheaf spaces. We will also explore various constructions and properties of these objects.

Series: PDE Seminar

This seminar concerns the analysis of a PDE, invented by J.M. Lasry
and P.L. Lions
whose applications need not concern us.
Notwithstanding, the focus of the application is the behavior of a
free boundary in a diffusion equation which has dynamically evolving,
non--standard sources. Global existence and uniqueness are
established for this system. The work to be discussed represents a
collaborative effort with
Maria del Mar Gonzalez, Maria Pia Gualdani and Inwon Kim.