Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, September 6, 2018.

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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 6, 2018

11:00 am in 241 Altgeld Hall,Thursday, September 6, 2018

#### $\alpha$-expansions with odd partial quotients

###### Florin Boca (UIUC)

Abstract: Nakada's $\alpha$-expansions interpolate between three classical continued fractions: regular (obtained at $\alpha=1$), Hurwitz singular (obtained at $\alpha$=little golden mean), and nearest integer (obtained at $\alpha$=1/2). This talk will consider $\alpha$-expansions in the situation where all partial quotients are asked to be odd positive integers. We will describe the natural extension of the underlying Gauss map and the ergodic properties of these transformations. This is joint work with Claire Merriman.

12:00 pm in 241 Altgeld Hall,Thursday, September 6, 2018

#### On "Closed subgroups generated by generic measure automorphisms" by S. Solecki, Part 1

###### Dakota Ihli (UIUC Math)

Abstract: We will read through this paper.

2:00 pm in 241 Altgeld,Thursday, September 6, 2018

#### A survey on primes in arithmetic progressions

###### Kyle Pratt (UIUC)

Abstract: I will give a survey talk on primes in arithmetic progressions. The talk should be accessible to any graduate student, number theorist or not.

4:00 pm in 245 Altgeld Hall,Thursday, September 6, 2018

#### Associahedra, cluster algebras, and scattering amplitudes

###### Hugh Thomas (University of Quebec at Montreal)

Abstract: The past several years have seen a flurry of activity in the physics of scattering amplitudes, in part motivated by a new geometric approach to the problem, which finds the solution encoded in a geometrical object, most famously in the amplituhedron of Arkani-Hamed and Trnka for N=4 super Yang-Mills. I will discuss a version of this approach for a simpler quantum field theory (biadjoint scalar $\varphi^3$ theory), where the geometrical object encoding the answer at tree level has recently been shown by Arkani-Hamed et al. to be an associahedron, a polytope originally defined by Jim Stasheff in the context of homotopy theory, and now well-known thanks to its connection to type $A_n$ cluster algebras. In recent work with my students Bazier-Matte, Chapelier, Douville, Mousavand, and former student Yıldırım, we showed that the construction of the associahedron developed by Arkani-Hamed et al. for their purposes is also applicable to other finite type cluster algebras, yielding simple constructions both of generalized associahedra, and, unexpectedly, of the Newton polytopes of the cluster variables. Time permitting, I will discuss the possibility (which we are investigating with Arkani-Hamed) that this construction in other types also has a physical interpretation.