Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, October 29, 2015.

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events for the
events containing

More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, October 29, 2015

11:00 am in 241 Altgeld Hall,Thursday, October 29, 2015

#### The Voronoi formula and double Dirichlet series

###### Fan Zhou (Ohio State University)

Abstract: We present a proof of Voronoi formula for coefficients of a large class of L-functions, in the style of the classical converse theorem of Weil. Our formula applies to full-level cusp forms, Rankin-Selberg convolutions, and certain isobaric sums. Our proof is based on the functional equations of L-functions twisted by Dirichlet characters and does not directly depend on automorphy. Hence it has wider application than any previous proofs. The key ingredient is the construction of a double Dirichlet series associated with these coefficients and the structure of nonprimitive Gauss/Ramanujan sums. This is joint work with Eren Mehmet Kıral.

1:00 pm in Altgeld Hall 243,Thursday, October 29, 2015

#### Energy growth in discontinuous Hamiltonian systems

###### Vadim Zharnitzky (UIUC Math)

Abstract: We consider a family of discontinuous area-preserving twist maps arising naturally in the study of non-smooth switched Hamiltonian systems. An unbounded solution for the special case of the so-called Pinball transformation is constructed. For the generic values of the parameters, in the large energy limit, the Pinball map is shown to behave similarly to another one introduced earlier by Erd\" os and Sz\" usz. This is a joint work with Maxim Arnold (UT Dallas).

2:00 pm in 347 Altgeld Hall,Thursday, October 29, 2015

#### The homotopy groups of the spectrum $tmf$

###### Dileep Menon (UIUC Math)

Abstract: In this talk we outline a procedure for calculating the homotopy groups of the spectrum $tmf$. We start by giving a brief description of $tmf$. Then we show there is a spectral sequence converging to the homotopy groups of $tmf$ whose $E_2$ page is the cohomology of the elliptic curve Hopf algebroid. We explain how we can understand all the differentials in this spectral sequence by understanding an important differential in the Adams-Novikov spectral sequence. We’ll work through the calculation at the prime 3 in detail.

3:00 pm in 243 Altgeld Hall,Thursday, October 29, 2015

#### Rees algebras of codimension three Gorenstein ideals

###### Bernd Ulrich (Purdue University)

Abstract: We study the implicit equations defining the image and the graph of rational maps between projective spaces, under the hypothesis that the base locus has codimension at most three and is defined by a Gorenstein ideal. We provide degree bounds for these implicit equations, and we describe them explicitly if the syzygies of the Gorenstein ideal are all linear. This is joint work with Andy Kustin and Claudia Polini.

4:00 pm in 245 Altgeld Hall,Thursday, October 29, 2015

#### Lecture 2. Quiver mutations and beyond

###### Sergey Fomin (Robert M. Thrall Collegiate Professor of Mathematics, University of Michigan)

Abstract: Quivers and their mutations provide a unifying framework for a variety of combinatorial transformations arising in different mathematical contexts: flips in triangulated surfaces, braid moves in pseudoline arrangements, etc. Several important results about quiver mutations are easy to state but surprisingly hard to prove. The dynamics of quiver mutations is the combinatorial engine that drives the algebraic dynamics of cluster transformations. Some examples of these dynamical systems, to be reviewed in the lecture, have fascinating periodicity and integrability properties. Based on joint work with D. Grigoriev, G. Koshevoy, P. Pylyavskyy, M. Shapiro, D. Thurston, and A. Zelevinsky.

5:00 pm in 245 Altgeld Hall,Thursday, October 29, 2015