Department of

Mathematics


Seminar Calendar
for events the day of Thursday, September 19, 2013.

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Thursday, September 19, 2013

12:30 pm in 464 Loomis Laboratory,Thursday, September 19, 2013

Braided tensor categories

Charles Rezk (Illinois Math)

Abstract: A gentle introduction to braided tensor categories. If time permits, I'll discuss fusion categories.

1:00 pm in Altgeld Hall 347,Thursday, September 19, 2013

Some combinatorial constructions in random groups

Danny Calegari (University of Chicago)

Abstract: We discuss some combinatorial (diagrammatic) methods for building subgroups in finitely presented groups. One immediate application is to the construction (almost surely) of certain kinds of subgroups in random groups (in the sense of Gromov), but I hope the method can be generalized, and in any case are of independent interest. Some of this represents joint work with Alden Walker and Henry Wilton.

2:00 pm in 149 Henry Administration Building,Thursday, September 19, 2013

Tools in studying behavior of sums of arithmetic functions over arithmetic progressions

Sneha Chaubey (UIUC Math)

Abstract: We begin with a brief discussion on problems and questions concerning the discrepancies of distributions when one compares the number of primes in different residue classes and give generalizations of the above problems for other arithmetic functions. We then discuss tools used in solving these problems. We will assume some knowledge about Dirichlet L-series and Riemann zeta function.

3:00 pm in 243 Altgeld Hall,Thursday, September 19, 2013

Local cohomology modules over polynomial rings of prime characteristic - Part II

Yi Zhang (UIUC)

Abstract: Let $R=k[x_1,\cdots, x_n]$ be a polynomial ring over a field $k$ of characteristic $p>0.$ If $I$ is an ideal of $R,$ we denote $H^i_I(R)$ the $i$-th local cohomology module of $R$ with support in $I.$ We discuss an adjointness theorem of Frobenius map. Then we use this property to study the dimension of the associated primes of $H^i_I(R),$ the grading on $H^i_{\mathfrak{m}}(H^j_I(R))$ in case $I$ is homogeneous and $\mathfrak{m}=(x_1,\cdots,x_n),$ and an algorithm to determine the vanishing of $H^i_{\mathfrak{m}}(H^j_I(R))$.

4:00 pm in 245 Altgeld Hall,Thursday, September 19, 2013

Most groups contain surface subgroups

Danny Calegari (University of Chicago)

Abstract: We show that "most" (finitely presented) groups (in a precise sense) contain subgroups which are isomorphic to the fundamental group of a closed oriented surface of genus at least 2. The subgroups can be constructed by a (reasonably) explicit and efficient procedure. The method of construction is interesting in its own right, and involves a mixture of combinatorics and probability theory.