Seminar Calendar
for Graduate Number Theory Seminar events the year of Friday, April 21, 2017.

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events for the
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Questions regarding events or the calendar should be directed to Tori Corkery.
      March 2017             April 2017              May 2017
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                      1       1  2  3  4  5  6
5  6  7  8  9 10 11    2  3  4  5  6  7  8    7  8  9 10 11 12 13
12 13 14 15 16 17 18    9 10 11 12 13 14 15   14 15 16 17 18 19 20
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Thursday, February 23, 2017

2:00 pm   in 241 Altgeld Hall,  Thursday, February 23, 2017
 Del Edit Copy
Submitted by amalik10.
 Dane Skabelund   [email] (UIUC)Some maximal curves obtained via a ray class field constructionAbstract: This talk will be about curves over finite fields which are "maximal" in the sense that they meet the Hasse-Weil bound. I will describe some problems relating to such curves, and give a description of some new "maximal" curves which may be obtained as covers of the Suzuki and Ree curves.

Tuesday, February 28, 2017

2:00 pm   in 241 Altgeld Hall,  Tuesday, February 28, 2017
 Del Edit Copy
Submitted by amalik10.
 Hannah Burson (UIUC)Weighted Partition IdentitiesAbstract: Ali Uncu and Alexander Berkovich recently completed some work proving several new weighted partition identities. We will discuss some of their theorems, which focus on the smallest part of partitions. Additionally, we will talk about some of the motivating work done by Krishna Alladi.

Thursday, March 9, 2017

2:00 pm   in 241 Altgeld Hall,  Thursday, March 9, 2017
 Del Edit Copy
Submitted by amalik10.
 Frank Garvan (University of Florida)Playing with partitions and $q$-seriesAbstract: We start with some open partition problems of Andrews related to Gauss's three triangular numbers theorem. We alter a generating function and find a new Hecke double sum identity. Along the way we need Bailey's Lemma and Zeilberger's algorithm. We finish with some even staircase partitions.

Thursday, April 6, 2017

2:00 pm   in 241 Altgeld Hall,  Thursday, April 6, 2017
 Del Edit Copy
Submitted by jli135.
 Kyle Pratt   [email] (UIUC)Primes with restricted digitsAbstract: Let $a_0 \in \{0,1,2,\ldots,9\}$ be fixed. James Maynard (2016) proved the impressive result that there are infinitely many primes without the digit $a_0$ in their decimal expansions. His theorem is a specific incarnation of a more general problem of finding primes in thin sequences. In this talk I will give a brief discussion about primes in thin sequences. I will also give an overview of some of the tools used in the course of Maynard's proof, including the Hardy-Littlewood circle method, Harman's sieve, and the geometry of numbers.

Tuesday, April 11, 2017

2:00 pm   in 241 Altgeld Hall,  Tuesday, April 11, 2017
 Del Edit Copy
Submitted by amalik10.
 Hsin-Po Wang (UIUC)Andrew's recent papers on integer partitions and the existence of combinatorial proofsAbstract: We will start with introducing some combinatorial notions; and then attack George E. Andrew's recent papers[1][2][3] to see if we can come up with some (simpler) combinatorial proofs. Despite the papers, we will show that under certain conditions, we can always translate an algebraic proof into a combinatorial proof. [1] G. Andrews and G. Simay. The mth Largest and mth Smallest Parts of a Partition. http://www.personal.psu.edu/gea1/pdf/307.pdf [2] G. Andrews and M. Merca. The Truncated Pentagonal Number Theorem. http://www.personal.psu.edu/gea1/pdf/288.pdf [3] G. Andrews, M Bech and N. Robbins. Partitions with Fixed Differences Between Larger and Smaller Parts. http://www.personal.psu.edu/gea1/pdf/305.pdf

Thursday, April 13, 2017

2:00 pm   in 241 Altgeld Hall,  Thursday, April 13, 2017
 Del Edit Copy
Submitted by jli135.
 Detchat Samart   [email] (UIUC)L-values, Bessel moments and Mahler measuresAbstract: We will discuss some formulas and conjectures relating special values of L-functions associated to modular forms to moments of Bessel functions and Mahler measures. Bessel moments arise in the study of Feynman integrals, while Mahler measures have received a lot of attention from mathematicians over the past few decades due to their apparent connection with number theory, algebraic geometry, and algebraic K-theory. Though easy to verify numerically with high precision, most of these formulas turn out to be ridiculously hard to prove, and no machinery working in full generality is currently known. Some available techniques which have been used to tackle these problems will be demonstrated. Time permitting, we will present a meta conjecture of Konstevich and Zagier which gives a general framework of how one could verify these formulas using only elementary calculus.

Thursday, April 20, 2017

 Andrew Sills (Georgia Southern University)MacMahon's partial fractionsAbstract: A. Cayley used ordinary partial fractions decompositions of $1/[(1-x)(1-x^2)\ldots(1-x^m)]$ to obtain direct formulas for the number of partitions of $n$ into at most $m$ parts for several small values of $m$. No pattern for general m can be discerned from these, and in particular the rational coefficients that appear in the partial fraction decomposition become quite cumbersome for even moderate sized $m.$ Later, MacMahon gave a decomposition of $1/[(1-x)(1-x^2). . .(1-x^m)]$ into what he called "partial fractions of a new and special kind" in which the coefficients are "easily calculable numbers" and the sum is indexed by the partitions of $m$. While MacMahon's derived his "new and special" partial fractions using "combinatory analysis," the aim of this talk is to give a fully combinatorial explanation of MacMahon's decomposition. In particular, we will observe a natural interplay between partitions of $n$ into at most $m$ parts and weak compositions of $n$ with $m$ parts.