Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, March 15, 2016.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    February 2016            March 2016             April 2016
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5  6          1  2  3  4  5                   1  2
7  8  9 10 11 12 13    6  7  8  9 10 11 12    3  4  5  6  7  8  9
14 15 16 17 18 19 20   13 14 15 16 17 18 19   10 11 12 13 14 15 16
21 22 23 24 25 26 27   20 21 22 23 24 25 26   17 18 19 20 21 22 23
28 29                  27 28 29 30 31         24 25 26 27 28 29 30



Tuesday, March 15, 2016

11:00 am in 243 Altgeld Hall,Tuesday, March 15, 2016

#### Picard groups of structured ring spectra and stable module categories

###### Akhil Mathew (Harvard)

Abstract: Let $G$ be a finite $p$-group. The stable module category of $G$ is defined as the quotient of the category of $G$-representations over a field $k$ of characteristic $p$ by those morphisms which factor through a projective. It can also be modeled as the category of module spectra over the Tate construction $k^{tG}$. It is a classical theorem of Dade that the Picard group of the stable module category contains no "exotic" objects when $G$ is abelian. This translates into a statement about the $E_\infty$-ring spectrum $k^{tG}$. We will discuss a general approach to studying the Picard groups of structured ring spectra using descent theory and describe a new proof of Dade's theorem based on Rognes's theory of Galois extensions of ring spectra and Galois descent.

12:00 pm in Altgeld Hall 243,Tuesday, March 15, 2016

#### SO(n,n+1) surface group representations

###### Brian Collier (UIUC Math)

Abstract: In this talk I will discuss a parameterization of n(2g-2) connected components of the SO(n,n+1) character variety of a closed surface of genus g. We will see how this parameterization generalizes both Hitchin's parameterization of the Hitchin component as a vector space of holomorphic differentials of degree 2,4,...,2n and Hitchin's parameterization of the nonzero Toledo invariant components of the PSL(2,R)=SO(1,2) Higgs bundle moduli space by holomorphic quadratic differentials twisted by an effective divisor.

1:00 pm in 345 Altgeld Hall,Tuesday, March 15, 2016

#### Distal and non-Distal Pairs

###### Travis Nell (UIUC)

Abstract: We will consider whether certain non-o-minimal expansions of o-minimal theories which are known to be NIP, are also distal. We observe that while tame pairs of o-minimal structures and the real field with a discrete multiplicative subgroup have distal theories, dense pairs of o-minimal structures and related examples do not.

3:00 pm in 241 Altgeld Hall,Tuesday, March 15, 2016

#### Hypergraph Turan numbers via Lagrangians and symmetrization

###### Tao Jiang (Miami University)

Abstract: Given an r-uniform hypergraph graph H, the Turan number ex(n, H) of H is the maximum size of an n-vertex r-uniform hypergraph G that does not contain H as a subgraph. We discuss some recent work by various authors, including myself and collaborators, on the exact determination (for large n) of ex(n, H) for many r-uniform hypergraphs H of a certain type using the method of hypergraph Lagrangians. We will mention some related problems.

4:00 pm in Altgeld Hall 159,Tuesday, March 15, 2016

#### Analytic Solution for Ratchet Guaranteed Minimum Death Benefit Options Under a Variety of Mortality Laws

###### Eric Ulm (Georgia State University)

Abstract: We derive a number of analytic results for GMDB ratchet options. Closed form solutions are found for De Moivre’s Law, Constant Force of Mortality, Constant Force of Mortality with an endowment age and constant force of mortality with a cutoff age. We find an infinite series solution for a general mortality laws and we derive the conditions under which this series terminates. We sum this series for at-the-money options under the realistic Makeham’s Law of Mortality.

4:00 pm in 243 Altgeld Hall,Tuesday, March 15, 2016

#### The Kempf-Ness theorem

###### Itziar Ochoa de Alaiza Gracia (UIUC Math)

Abstract: Given a linear action of a reductive group $G$ on a smooth, projective variety $X \subset \mathbb{P}^n$, one can define the GIT quotient, which is a good quotient of the action of $G$ on $X^{ss}$. On the other hand, we can also consider the symplectic reduction of $X$ by a maximal real compact Lie subgroup of $G$. Then the Kempf-Ness theorem states that these two approaches give the same quotient. In this talk I will define the GIT and symplectic quotients and conclude with the Kempf-Ness theorem.