Seminars and Colloquia by Series

Circle homeomorphisms with singularity points.

Series
CDSNS Colloquium
Time
Monday, April 16, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Akhtam Djalilov – Univ. of Samarkand and CUNY Stony Brook
An important question in circle dynamics is regarding the absolute continuity of an invariant measure. We will consider orientation preserving circle homeomorphisms with break points, that is, maps that are smooth everywhere except for several singular points at which the first derivative has a jump. It is well known that the invariant measures of sufficiently smooth circle dieomorphisms are absolutely continuous w.r.t. Lebesgue measure. But in the case of homeomorphisms with break points the results are quite dierent. We will discuss conjugacies between two circle homeomorphisms with break points. Consider the class of circle homeomorphisms with one break point b and satisfying the Katznelson-Ornsteins smoothness condition i.e. Df is absolutely continuous on [b; b + 1] and D2f 2 Lp(S1; dl); p > 1: We will formulate some results concerning the renormaliza- tion behavior of such circle maps.

Discrete Mathematical Biology Working Seminar

Series
Other Talks
Time
Monday, April 16, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Svetlana Poznanovik – Georgia Tech
A discussion of the paper "Evaluation of the information content of RNA structure mapping data for secondary structure prediction" by Quarrier et al (RNA, 2010).

The size of a hypergraph and its matching number

Series
Combinatorics Seminar
Time
Friday, April 13, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Huang Hao – Math, UCLA
More than 40 years ago, Erdos asked to determine the maximum possible number of edges in a k-uniform hypergraph on n vertices with no matching of size t (i.e., with no t disjoint edges). Although this is one of the most basic problem on hypergraphs, progress on Erdos' question remained elusive. In addition to being important in its own right, this problem has several interesting applications. In this talk we present a solution of Erdos' question for t

Plane fields on 3-manifolds III

Series
Geometry Topology Working Seminar
Time
Friday, April 13, 2012 - 14:00 for 2 hours
Location
Skiles 006
Speaker
John Etnyre – Ga Tech

Please Note: Note this is a 2 hour talk.

In this series of talks I will discuss various special plane fields on 3-manifold. Specifically we will consider folaitions and contact structures and the relationship between them. We will begin by sketching a proof of Eliashberg and Thurston's famous theorem from the 1990's that says any sufficiently smooth foliation can be approximated by a contact structure. In the remaining talks I will discuss ongoing research that sharpens our understanding of the relation between foliations and contact structures.

Variational problems and PDEs arising in congested transport models

Series
PDE Seminar
Time
Thursday, April 12, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Guillaume Carlier – Universite de Paris IX (Paris-Dauphine)
In this talk, I will describe several models arising in congested transport problems. I will first describe static models which lead to some highly degenerate elliptic PDEs. In the second part of the talk, I will address dynamic models which can be seen as a generalization of the Benamou-Brenier formulation of the quadratic optimal transport problem and will discuss the existence and regularity of the adjoint state. The talk will be based on several joint works with Lorenzo Brasco, Pierre Cardaliaguet, Bruno Nazaret and Filippo Santambrogio.

Horocycle flows on $\Gamma/SL(2, \mathbb{R}$.

Series
Dynamical Systems Working Seminar
Time
Wednesday, April 11, 2012 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Mikel J. De Viana – Georgia Tech.
In the 1990's Marina Ratner published a famous series of papers showing that ergodic measures invariant under unipotent flows over quotients $\Gamma/G$ are homogeneous. From this, she deduced many other remarkable properties for these flows (e.g that the closure of orbits are homogeneous and that orbits are uniformly distributed in their closures). To prove this result will require several lectures, but already the case of horocycle flow in $\Gamma/SL(2, \mathbb{R})$ presents several or her ideas. In this talk we will present the ideas of the proof in this case and present an application due to Margulis.

The s-Riesz transform of an s-dimensional measure in R^2 is unbounded for 1<s<2

Series
Analysis Seminar
Time
Wednesday, April 11, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Vladimir Eiderman – University of Wisconsin
This is a joint work with F.~Nazarov and A.~Volberg.Let $s\in(1,2)$, and let $\mu$ be a finite positive Borel measure in $\mathbb R^2$ with $\mathcal H^s(\supp\mu)<+\infty$. We prove that if the lower $s$-density of $\mu$ is+equal to zero $\mu$-a.~e. in $\mathbb R^2$, then$\|R\mu\|_{L^\infty(m_2)}=\infty$, where $R\mu=\mu\ast\frac{x}{|x|^{s+1}}$ and $m_2$ is the Lebesque measure in $\mathbb R^2$. Combined with known results of Prat and+Vihtil\"a, this shows that for any noninteger $s\in(0,2)$ and any finite positive Borel measure in $\mathbb R^2$ with $\mathcal H^s(\supp\mu)<+\infty$, we have+$\|R\mu\|_{L^\infty(m_2)}=\infty$.Also I will tell about the resent result of Ben Jaye, as well as about open problems.

Elasto-Capillarity

Series
Research Horizons Seminar
Time
Wednesday, April 11, 2012 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
John McCuan – Georgia Tech
Classical mathematical capillarity theory has as its foundation variational methods introduced by Gauss. There was a heuristic explanation given earlier by Thomas Young, and his explanations did have quantitative scientific content. Due partially to their simplistic nature, the explanations of Young live on today in engineering textbooks, though in certain cases it has been pointed out that they lead to anomolous predictions (which are effectively avoided in the Gaussian variational framework). I will discuss a fundamentally new direction in mathematical capillarity which is motivated by an effort to harmonize the heuristic and rigorous elements of the theory and has other important applications as well.

On Aleksandrov-Bakelman-Pucci type estimates for integro-differential equations

Series
PDE Seminar
Time
Tuesday, April 10, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Russell Schwab – Carnegie Mellon University
Despite much recent (and not so recent) attention to solutions of integro-differential equations of elliptic type, it is surprising that a result such as a comparison theorem which can deal with only measure theoretic norms (e.g. L-n and L-infinity) of the right hand side of the equation has gone unexplored. For the case of second order equations this result is known as the Aleksandrov-Bakelman-Pucci estimate (and dates back to circa 1960s), which says that for supersolutions of uniformly elliptic equation Lu=f, the supremum of u is controlled by the L-n norm of f (n being the underlying dimension of the domain). We will discuss this estimate in the context of fully nonlinear integro-differential equations and present a recent result in this direction. (Joint with Nestor Guillen, available at arXiv:1101.0279v3 [math.AP])

Galois groups of Schubert problems of lines are at least alternating

Series
Algebra Seminar
Time
Tuesday, April 10, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Abraham Martin del Campo – Texas A&amp;amp;M
The Galois group of a problem in enumerative geometry is a subtle invariant that encodes special structures in the set of solutions. This invariant was first introduced by Jordan in 1870. In 1979, Harris showed that the Galois group of such problems coincides with the monodromy group of the total space. These geometric invariants are difficult to determine in general. However, a consequence of Vakil's geometric Littlewood-Richardson rule is a combinatorial criterion to determine if a Schubert problem on a Grassmannian contains at least the alternating group. Using Vakil's criterion, we showed that for Schubert problems of lines, the Galois group is at least the alternating group.

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