Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, October 1, 2014.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    September 2014          October 2014          November 2014
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1  2  3  4  5  6             1  2  3  4                      1
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Wednesday, October 1, 2014

2:00 pm in 441 Altgeld Hall,Wednesday, October 1, 2014

#### What are Rees algebras?

###### Eliana Duarte   [email] (UIUC Math)

Abstract: The study of Rees algebras plays an important role in the implicitization problem for maps between projective spaces. In this talk I will define the Rees algebra of an ideal in a commutative ring and explain its relation to implicitization of curves and surfaces. All of the concepts just mentioned will be defined and illustrated with friendly examples.

2:00 pm in 443 Altgeld Hall,Wednesday, October 1, 2014

#### Fundamental solution of kinetic Fokker-Planck operator with anisotropic nonlocal dissipativity

###### Xicheng Zhang (Wuhan University Math)

Abstract: By using a probability approach (the Malliavin calculus), we prove the existence of smooth fundamental solutions for degenerate kinetic Fokker-Planck equation with anisotropic nonlocal dissipativity, where the dissipative term is the generator of an anisotropic L\'evy process, and the drift term is allowed to be cubic growth.

3:00 pm in 347 Altgeld Hall,Wednesday, October 1, 2014

#### Maximal green sequences for cluster algebra structures on double Bruhat cells

###### Milen Yakimov (Louisiana State University)

Abstract: Maximal green sequences of cluster mutations were introduced by Keller for the purposes of applications to quantum Donaldson-Thomas invariants, and by string theorists for the study of BPS spectra. It is conjectured that they are in bijection with discrete stability conditions with finitely many stables on the corresponding cluster category (under certain identifications). We will prove that maximal green sequences exist for all Berenstein-Fomin-Zelevinsky cluster algebras associated to double Bruhat cells in arbitrary simple Lie groups. This is a large class of cluster algebras that plays an important role in Lie theory.

4:00 pm in 245 Altgeld Hall,Wednesday, October 1, 2014

#### An Introduction to Symplectic Topology

###### Ely Kerman (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: Mechanical systems which preserve energy also preserve volumes in phase space. In 1890 Poincar\'e exploited this property to prove his famous recurrence theorem. In fact these mechanical systems preserve a more subtle "symplectic" structure which corresponds to the measurement of certain two-dimensional areas. The consequences of this latter preservation lie at the heart of symplectic topology. They are varied and easily described but are usually very difficult to prove. In this talk I will describe several of the remarkable theorems of symplectic topology, like Gromov's Nonsqueezing Theorem, outline the ideas involved in their proof and hopefully mention some open questions including a conjectured generalization of Poincar\'e's recurrence theorem.