Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, December 3, 2013.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    November 2013          December 2013           January 2014
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1  2    1  2  3  4  5  6  7             1  2  3  4
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Tuesday, December 3, 2013

1:00 pm in 345 Altgeld Hall,Tuesday, December 3, 2013

#### O-minimality of some quasianalytic algebras of functions

###### Santiago Camacho (UIUC)

Abstract: Functions definable in o-minimal structures behave rather nicely except for a "small" set of the ambient space they are defined. In particular for any function $f$ on $R$, the universe of an o-minimal structure, and almost every nice property of functions and every point $a \in R$ there is an open interval with $a$ in its frontier, such that $f$ has that property inside the interval. It is to be noted that quasianalitycity of a system of functions does not imply directly o-minimality of the structure they generate. We then consider a set of conditions on a quasianalytic system of algebras of functions together with an $\mathbb{R}$-algebra embedding from their germs to the ring of generalized power series. If these germs together with the embedding satisfy certain properties, we get o-minimality of the structure the original functions generate.

2:00 pm in Altgeld Hall 347,Tuesday, December 3, 2013

#### Sharp maximal inequalities for semimartingales

Abstract: In the nineties, Burkholder introduced a beautiful method which enables us to deduce sharp maximal inequalities for martingale transforms and stochastic integrals from the existence of solutions to certain nonlinear problems. We will discuss this method as well as its extensions which lead to estimates for more general class of semimartingales. We will illustrate the technique by proving several exemplary sharp inequalities.

3:00 pm in 241 Altgeld Hall,Tuesday, December 3, 2013

#### A Proof of the Manickam-Miklos-Singhi Conjecture for Vector Spaces

###### Ameera Chowdhury   [email] (Carnegie Mellon)

Abstract: Let $V$ be an $n$-dimensional vector space over a finite field. Assign a real-valued weight to each $1$-dimensional subspace in $V$ so that the sum of all weights is zero. Define the weight of a subspace $S \subset V$ to be the sum of the weights of all the $1$-dimensional subspaces it contains. We prove that if $n \geq 3k$, then the number of $k$-dimensional subspaces in $V$ with nonnegative weight is at least the number of $k$-dimensional subspaces in $V$ that contain a fixed $1$-dimensional subspace. This result verifies a conjecture of Manickam and Singhi from 1988. Joint work with Ghassan Sarkis (Pomona College) and Shahriar Shahriari (Pomona College).

3:00 pm in 243 Altgeld Hall,Tuesday, December 3, 2013

#### Construction of the second flip of $M_{g}$

###### David Smyth (ANU)

Abstract: I will discuss aspects of the construction of the second flip in the log minimal model program for $M_{g}$ (joint with Alper, Fedorchuk, van der Wyck). I will focus on the way in which formal local VGIT is used to construct the second flip as an algebraic space.

4:00 pm in 243 Altgeld Hall,Tuesday, December 3, 2013

#### The Étale Fundamental Group

###### Matej Penciak (UIUC Math)

Abstract: The purpose of this talk is to introduce the étale fundamental group of a scheme. Taking the Galois theory of fields and the theory of covering spaces as our guides, we will explore their generalizations to the setting of schemes. After defining the étale fundamental group, we will give an idea of how these groups may be computed.