Department of

Mathematics


Seminar Calendar
for events the day of Wednesday, October 16, 2013.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, October 16, 2013

12:00 pm in in Grainger Library, Room 335,Wednesday, October 16, 2013

A Geometric Interpretation and Proof of Baum's Algorithm for Estimation of the Parameters of a Probabilistic Function of a Markov Process and,Talbot effect for a nonlinear Schrödinger equation on the torus.

Steven Levinson, ECE and Nikolaos Tzirakis , Math

Abstract: Two talks will be given: Steven Levinson, ECE, talks on A Geometric Interpretation and Proof of Baum's Algorithm for Estimation of the Parameters of a Probabilistic Function of a Markov Process,followed by Nikolaos Tzirakis , Math, reporting on Talbot effect for a nonlinear Schrödinger equation on the torus.

3:00 pm in 143 Altgeld Hall,Wednesday, October 16, 2013

T-systems, Plucker coordinates and Pentagram maps

Panupong Vichitkunakorn (UIUC Math)

Abstract: An $A_\infty$ T-system is a system satisfying the octahedron relation. Any solutions of a half-plane $A_\infty$ T-system can be written as discrete Wronskians of the initial conditions. Using these facts, I will write the octahedron relation as a Plucker relation, and the T-system solutions are then expressed as Plucker coordinates of an infinite-dimensional grassmannian. Lastly, I will write the pentagram maps as T-systems. This gives us another coordinates of the pentagram maps.

4:00 pm in 245 Altgeld Hall,Wednesday, October 16, 2013

Independent sets in hypergraphs

Jozsef Balog (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: Many important theorems and conjectures in combinatorics, such as the theorem of Szemeredi on arithmetic progressions and the Erdos-Stone Theorem in extremal graph theory, can be phrased as statements about families of independent sets in certain uniform hypergraphs. In recent years, an important trend in the area has been to extend such classical results to the so-called 'sparse random setting'. This line of research has recently culminated in the breakthroughs of Conlon and Gowers and of Schacht, who developed general tools for solving problems of this type. Although these two papers solved very similar sets of longstanding open problems, the methods used are very different from one another and have different strengths and weaknesses. In this talk, we explain a third, completely different approach to proving extremal and structural results in sparse random sets that also yields their natural `counting' counterparts. We give a structural characterization of the independent sets in a large class of uniform hypergraphs. Joint work with Robert Morris and Wojciech Samotij.