Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, September 21, 2017.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, September 21, 2017

11:00 am in 241 Altgeld Hall,Thursday, September 21, 2017

#### 4-Shadows in q-Series: Gupta, Kimberling, the Garden of Eden and the OEIS.

###### George Andrews (Penn State )

Abstract: This talk is devoted to discussing the implications of a very elementary technique for proving mod 4 congruences in the theory of partitions. It starts with a tribute to the late Hans Raj Gupta and leads in unexpected ways to partitions investigated by Clark Kimberling, to Bulgarian Solitaire, and to Garden of Eden partitions. Each surprise busts forth from the OEIS

12:00 pm in Altgeld Hall 243,Thursday, September 21, 2017

#### Pair correlation in Apollonian circle packings

###### Xin Zhang (University of Illinois at Urbana-Champaign)

Abstract: Consider four mutually tangent circles, one containing the other three. An Apollonian circle packing is formed when the remaining curvilinear triangular regions are recursively filled with tangent circles. The extensive study of this object in the last fifteen years has led to many beautiful theorems in number theory, graph theory, and homogeneous dynamics. In this talk I will discuss a new type of problems, which concern the fine scale structure of Apollonian circle packings. In particular, I will show that the limiting pair correlation of circles exists. A critical tool we use is an extended version of a theorem of Mohammadi-Oh on the equidistribution of expanding horospheres in infinite volume hyperbolic spaces. This work is motivated by an IGL project that I mentored in Spring 2017.

12:30 pm in 276 Loomis,Thursday, September 21, 2017

#### Soft particles in Effective Field Theories

###### Henriette Elvang (University of Michigan)

Abstract: I will discuss the approach to study quantum field theories using the soft limits of massless particles. In particular, I will present modifications to classic soft theorems for photons and gravitons that arise from higher-dimension operators in effective field theories; these can be interpreted as the corrections from loops of massive particles. Finally I will discuss on-going work on using soft limits to examine the landscape of effective field theories with enhanced symmetry.

4:00 pm in 245 Altgeld Hall,Thursday, September 21, 2017

#### The Man Who Knew Infinity: the Movie, the Man, and the Mathematics

###### George Andrews (Penn State)

Abstract: In the spring of 2016, the motion picture, The Man Who Knew Infinity, was released. It is now available on DVD. The movie tells the life story of the Indian genius, Ramanujan. In this talk, I hope to start with the trailer from the movie. Then I shall provide a brief discussion of Ramanujan's life with a glimpse of the mathematics contained in his celebrated Lost Notebook (of which Bruce Berndt and I have just concluded preparing the fifth and final volume explicating the many assertion therein). The bulk of the talk will consider the path from the Rogers-Ramanujan identities to current open problems and how computer algebra assists in their study.