Seminar Calendar
for Number Theory events the next 12 months of Sunday, January 1, 2017.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, January 19, 2017

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, January 19, 2017
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Submitted by sahlgren.
Joel Specter (Northwestern University)
Commuting Endomorphisms of the p-adic Formal Disk
Abstract: Any one dimensional formal group law over $\mathbb{Z}_p$ is uniquely determined by the series expansion of its multiplication by $p$ map. This talk addresses the converse question: when does an endomorphism $f$ of the $p$-adic formal disk arise as the multiplication by $p$-map of a formal group? Lubin, who first studied this question, observed that if such a formal group were to exist, then $f$ would commute with an automorphism of infinite order. He formulated a conjecture under which a commuting pair of series should arise from a formal group. Using methods from p-adic Hodge theory, we prove the height one case of this conjecture.

Tuesday, January 24, 2017

Graduate Student Number Theory Seminar
2:00 pm   in 241 Altgeld Hall,  Tuesday, January 24, 2017
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Submitted by amalik10.
Byron Heersink (UIUC)
Poincaré sections for the horocycle flow in covers of SL(2,$\mathbb{R}$)/SL(2,$\mathbb{Z}$) and applications to Farey fraction statistics
Abstract: For a given finite index subgroup $H\subseteq$SL(2,$\mathbb{Z}$), we use a process developed by Fisher and Schmidt to lift a Poincaré section of the horocycle flow on SL(2,$\mathbb{R}$)/SL(2,$\mathbb{Z}$) found by Athreya and Cheung to the finite cover SL(2,$\mathbb{R}$)/$H$ of SL(2,$\mathbb{R}$)/SL(2,$\mathbb{Z}$). We then relate the properties of this section to the gaps in Farey fractions and describe how the ergodic properties of the horocycle flow can be used to obtain certain statistical properties of various subsets of Farey fractions.

Thursday, February 2, 2017

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, February 2, 2017
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Submitted by sahlgren.
Bruce Berndt (Illinois Math)
Identities
Abstract: As the title suggests, this lecture features mathematical identities. The identities we have chosen (we hope) are interesting, fascinating, surprising, and beautiful! Many of the identities are due to Ramanujan. Topics behind the identities include partitions, continued fractions, sums of squares, theta functions, Bessel functions, $q$-series, other infinite series, and infinite integrals.

Thursday, February 9, 2017

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, February 9, 2017
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Submitted by sahlgren.
Matthias Strauch (Indiana University Bloomington)
Coverings of the p-adic upper half plane and arithmetic differential operators
Abstract: The p-adic upper half plane comes equipped with a remarkable tower of GL(2)-equivariant etale covering spaces, as was shown by Drinfeld. It has been an open question for some time whether the spaces of global sections of the structure sheaf on such coverings provide admissible locally analytic representations. Using global methods and the p-adic Langlands correspondence for GL(2,Qp), this is now known to be the case by the work of Dospinescu and Le Bras. For the first layer of this tower Teitelbaum exhibited a nice formal model which we use to provide a local proof for the admissibility of the representation (when the base field is any finite extension of Qp). The other key ingredients are suitably defined sheaves of arithmetic differential operators and D-affinity results for formal models of the rigid analytic projective line, generalizing those of Christine Huyghe. This is joint work with Deepam Patel and Tobias Schmidt.

Thursday, February 23, 2017

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, February 23, 2017
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Submitted by sahlgren.
Amita Malik (Illinois Math)
Partitions into $k$th powers of a fixed residue class
Abstract: G. H. Hardy and S. Ramanujan established an asymptotic formula for the number of unrestricted partitions of a positive integer, and claimed a similar asymptotic formula for the number of partitions into perfect $k$th powers, which was later proved by E. M. Wright. In this talk, we discuss partitions into parts from a specific set $A_k(a_0,b_0) :=\left\{ m^k : m \in \mathbb{N}, m\equiv a_0 \pmod{b_0} \right\}$, for fixed positive integers $k$, $a_0,$ and $b_0$. We give an asymptotic formula for the number of such partitions, thus generalizing the results of Wright and others. We also discuss the parity problem for such partitions. This is joint work with Bruce Berndt and Alexandru Zaharescu.

Graduate Number Theory Seminar
2:00 pm   in 241 Altgeld Hall,  Thursday, February 23, 2017
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Submitted by amalik10.
Dane Skabelund   [email] (UIUC)
Some maximal curves obtained via a ray class field construction
Abstract: 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.

Thursday, March 2, 2017

Number Theory Seminar
11:00 am   in Altgeld Hall,  Thursday, March 2, 2017
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Submitted by sahlgren.
Brad Rodgers (University of Michigan)
Sums in short intervals and decompositions of arithmetic functions
Abstract: In this talk we will discuss some old and new conjectures about the behavior of sums of arithmetic functions in short intervals, along with analogues of these conjectures in a function field setting that have been proved in recent years. We will pay particular attention to some surprising phenomena that comes into play, and a decomposition of arithmetic functions in a function field setting that helps elucidate what's happening.

Thursday, March 9, 2017

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, March 9, 2017
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Submitted by sahlgren.
Frank Garvan (University of Florida)
To Be Announced

Thursday, March 16, 2017

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, March 16, 2017
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Submitted by sahlgren.
Armin Straub (University of South Alabama)
To Be Announced

Thursday, March 30, 2017

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, March 30, 2017
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Submitted by sahlgren.
Preston Wake (University of California at Los Angeles)
To Be Announced

Thursday, April 6, 2017

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, April 6, 2017
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Submitted by sahlgren.
Bao V. Le Hung (University of Chicago)
To Be Announced

Thursday, April 13, 2017

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, April 13, 2017
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Submitted by sahlgren.
Matt Papanikolas (Texas A&M University)
To Be Announced

Thursday, April 20, 2017

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, April 20, 2017
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Submitted by sahlgren.
Robert Lemke Oliver (Tufts University)
To Be Announced

Thursday, April 27, 2017

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, April 27, 2017
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Submitted by sahlgren.
Andrew Sills (Georgia Southern University)
To Be Announced