Department of

# Mathematics

Seminar Calendar
for events the day of Monday, March 31, 2014.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, March 31, 2014

2:00 pm in 147 Altgeld Hall,Monday, March 31, 2014

#### Singularities of Hinge Structures

###### Victoria Blumen (UIUC Math)

Abstract: I will discuss the paper "Singularities of Hinge Structures" by Ciprian Borcea and Ileana Streinu. This paper studies the singularities of maps associated to the body and hinge structure and panel and hinge structure that is often seen in certain protein chains and other molecular conformations. Several proofs important to robotics research are included and elaborated upon in general dimension.

3:00 pm in 145 Altgeld Hall,Monday, March 31, 2014

#### Dynamical convexity and elliptic orbits for Reeb flows

###### Miguel Abreu (Instituto Superior Técnico)

Abstract: A classical conjecture states that any convex hypersurface in even-dimensional euclidean space carries an elliptic closed orbit of its characteristic flow. Dell'Antonio-D'Onofrio-Ekeland proved it in 1995 for antipodal invariant convex hypersurfaces. In this talk I will present a generalization of this result using contact homology and a notion of dynamical convexity first introduced by Hofer-Wysocki-Zehnder for contact forms on the 3-sphere. Applications include certain geodesic flows, magnetic flows and toric contact manifolds. This is joint work with Leonardo Macarini.

4:00 pm in 143 Altgeld Hall,Monday, March 31, 2014

#### The Seiberg-Witten solution

###### Sheldon Katz (Illinois Math)

Abstract: Last time we saw how supersymmetric gauge theories can be described by families of elliptic curves. I follow the original method of Seiberg and Witten solution to describe the quantum moduli space of N=2 SU(2) gauge theory, relating quantum calculations to monodromies of families of elliptic curves, arriving at the family $y^2=(x-u)(x^2-\Lambda^4)$ which solves the theory.

4:00 pm in 241 Altgeld Hall,Monday, March 31, 2014

#### Nonlinear patterns in large sets of countable fields

###### Joel Moreira (Ohio State)

Abstract: An old lemma of Schur states that given any finite partition of the positive integer numbers, there exists a triple of the form {x,y,x+y} in the same cell of the partition. It follows that there exists a triple of the form {x,y,xy} in the same cell, but it has been an open problem ever since whether one can surely find a quadruple {x,y,x+y,xy} in the same cell. I will describe a dynamical approach to this type of problems and present recent joint work with V. Bergelson on analogues of this and similar questions with the set of positive integers replaced with a field.

5:00 pm in 241 Altgeld,Monday, March 31, 2014

#### Module version of Kirchberg's theory

###### Jian Liang (UIUC Math)

Abstract: In this talk, we will present our recent results about module version of Kirchberg's theory. We will introduce the notion of module WEP and show some basic properties and examples. This is a joint work with Sepideh Rezvani.