Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, October 4, 2018.

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Questions regarding events or the calendar should be directed to Tori Corkery.
    September 2018          October 2018          November 2018
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30


Thursday, October 4, 2018

11:00 am in 241 Altgeld Hall,Thursday, October 4, 2018

#### Dirichlet L-functions of quadratic characters of prime conductor at the central point

###### Siegfred Baluyot (Illinois Math)

Abstract: In this joint work with Kyle Pratt, we prove that more than nine percent of the central values $L(\frac{1}{2},\chi_p)$ are non-zero, where $p\equiv 1$ (mod $8$) ranges over primes and $\chi_p$ is the real primitive Dirichlet character of conductor $p$. Previously, it was not known whether a positive proportion of these central values are non-zero. As a by-product, we obtain estimates for the second and third moments of $L(\frac{1}{2},\chi_p)$.

12:30 pm in 464 Loomis,Thursday, October 4, 2018

#### To Be Announced

###### Jim Halverson (Northeastern)

2:00 pm in 241 Altgeld Hall,Thursday, October 4, 2018

#### The distribution of elementary symmetric polynomials over finite fields

###### Oscar E. Gonzalez (Illinois Math)

Abstract: The elementary symmetric polynomial of degree k in n variables is formed by adding all distinct products of k distinct variables. In 1950, N. J. Fine proved that these polynomials (mod p) have an asymptotic distribution and gave precise results in the cases p=2 and p= 3. In this talk we will discuss several results and conjectures about the distribution of elementary symmetric polynomials over finite fields, with special attention to the finite field of two elements.

3:00 pm in 345 Altgeld Hall,Thursday, October 4, 2018

#### On the quadratic dual of the Fomin-Kirillov algebras

###### Chelsea Walton   [email] (University of Illinois)

Abstract: The first half of this talk will be a brief review of nice ring-theoretic and homological properties of noncommutative graded algebras. Then we will apply this discussion to the study of the quadratic dual of the Fomin-Kirillov algebras. Open questions will be provided at the end. This is joint work with James Zhang.