Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, November 4, 2014.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, November 4, 2014

11:00 am in 243 Altgeld Hall,Tuesday, November 4, 2014

#### Higher Associativity of Moore spectra

###### Prasit Bhattacharya   [email] (Indiana University)

Abstract: Not much is known about homotopy coherent ring structures of the Moore spectrum $M_p(i)$ (the cofiber of $p^i$ self-map on the sphere spectrum $S^0$), especially when $i > 1$. Stasheff developed a hierarchy of coherence for homotopy associative multiplications called $A_n$ structures. The only known results are that $M_p(1)$ is $A_{p-1}$ and not $A_p$ and that $M_2(i)$ are at least $A_3$ for $i>1$. In this talk, techniques will be developed to get estimates of `higher associativity' structures on $M_p(i)$.

1:00 pm in 345 Altgeld Hall,Tuesday, November 4, 2014

#### Generic orbits and type isolation in the Gurarij space

###### Ward Henson (UIUC, UC Berkeley)

Abstract: This is joint work with Itai Ben Yaacov of Lyon, focused on the model theory of Gurarij's separable universal Banach space. It has been known for awhile that in continuous model theory the Gurarij space is a very nice Fraisse limit---it's theory is separably categorical and has quantifier elimination. We have written clear and simple proofs of all those basic facts, and also have been studying the type spaces for this theory, over an arbitrary set of parameters, which we may as well take to be a separable Banach space $E$. Our main achievement is to completely characterize isolated types in the type spaces over $E$, using tools from convex analysis. This lets us derive a lot of information about the situation in which the set of isolated types is dense (for the logic topology) and hence there is an embedding $T$ of $E$ into the Gurarij space $G$ such that the structure $(G,T(e) : e \in E)$ is atomic; this is the same as saying there is a generic orbit in the Polish space of all such embeddings, under the action of ${\rm Aut}(G)$. For example this happens for any $E$ of dimension $\leq 3$, for any finite dimensional E that is smooth or polyhedral, but not for all $E$---we give an $E$ of dimension $4$ such that the isolated types over $E$ are not dense, and we show that over many familiar infinite dimensional spaces $E$, there are no isolated types except for the obvious ones (coming from elements of $E$). The tools from convex analysis that we develop should help answer several open questions about the Gurarij space, such as: how complex is the space of orbits of the action of ${\rm Aut}(G)$ on the unit sphere of $G$? (We can derive a new result, that there are infinitely many orbits, but this is far from giving the final story.)

1:00 pm in Altgeld Hall 243,Tuesday, November 4, 2014

#### Themes and directions in Alexandrov geometry

###### Stephanie Alexander (UIUC Math)

Abstract: This talk will introduce the basics of Alexandrov geometry through examples, and present some personal favorite themes, applications and possible future directions. A run-through of an upcoming Berlin Math School colloquium aimed at a broad spectrum of mathematicians including graduate students. Grad students very welcome! View talk at http://youtu.be/vp4GZuqUWtE

3:00 pm in 243 Altgeld Hall,Tuesday, November 4, 2014

#### Quantization and Reduction mod p

###### Chris Dodd (University of Toronto)

Abstract: I will discuss some conjectures of A. Belov-Kanel and M. Kontsevich concerning the structure of the automorphism group of the Weyl algebra. The key turns out to be defining an appropriate notion of "support cycle" for a D-module, which, as it turns out, is not necessarily conical. In particular, we shall discuss a "quantization correspondence" which is based on reducing D-modules to finite characteristic.

3:00 pm in 241 Altgeld Hall,Tuesday, November 4, 2014

#### The Typical Structure of Intersecting Families

###### Michelle Delcourt   [email] (UIUC Math)

Abstract: Enumerating families of combinatorial objects with given properties and describing the typical structure of these objects are fundamental problems in extremal combinatorics. During this talk, we will focus in particular on the structure of t-intersecting families of permutations on [n]. If time permits, we will explore the structure of intersecting families in a variety of other settings. Main tools include generalizations of the Bollobás set-pairs inequality and Ellis's stability theorem for intersecting families of permutations. This is joint work with József Balogh, Shagnik Das, Hong Liu, and Maryam Sharifzadeh.

4:00 pm in 2 Illini Hall,Tuesday, November 4, 2014

#### Analytic Approximations of Risk Measures of Variable Annuity Guaranteed Benefit

###### Bingji Yi (UIUC Math)

Abstract: Guaranteed Minimum Accumulation Benefit is a complicated, multi-period, Asian option like guaranteed benefit offered by variable annuity products. Due to its complexity, the prevalent method of risk management in practice is Monte Carlo simulation. However, the simulation methods could be costly and time-consuming. To find efficient solutions for risk measures, we use a hybrid of several analytical methods including spectral expansion techniques and discrete convolution approximations. Moreover, to improve computational efficiency, we also use Laplace inversion methods. This is joint work with Dr. Runhuan Feng.