# Queen's University - Department of Mathematics and Statistics

 Wednesday, November 15 Number Theory Seminar Time: 1:30 p.m. Place: Jeffery 319 Speaker: Peng-Jie Wong, University of Lethbridge Title: Base change and the Langlands reciprocity conjecture Abstract Attached Thursday, November 16 Seminar in Free Probability and Random Matrices Time: 3:30 p.m. Place: Jeffery 222 Speaker: Pei-Lun Tseng, Queen’s University Title: Free independence of type B Abstract Attached Friday, November 17 Department Colloquium Time: 2:30 p.m. Place: Jeffery 234 Speaker: Mokshay Madiman, University of Delaware Title: The convexifying effect of Minkowski summation Abstract Attached Monday, November 20 Special Colloquium Time: 4:30 p.m. Place: Jeffery 118 Speaker: Alex Wright, Stanford University Title: Dynamics, geometry, and the moduli space of Riemann surfaces Abstract Attached Wednesday, November 22 Special Colloquium Time: 3:30 p.m. Place: Jeffery 234 Speaker: Jenny Wilson Title: Stability in ordered configuration spaces Abstract Attached Friday, November 24 Ph.D. Thesis Defense Time: 10:00 a.m. Place: Jeffery 521 Ph.D. Student: Aaron Springford Title: Spectral analysis of time series with latent and irregular times Supervisors: D. Thomson and G. Takahara

Items for the Info Sheet should reach Anne ( burnsa@queensu.ca) by noon on Monday. The Info Sheet is published every Tuesday.

Wednesday, November 15, 1:30 p.m. Jeffery 319 - Number Theory Seminar

Speaker: Peng-Jie Wong

Title: Base change and the Langlands reciprocity conjecture

Abstract: In light of Artin reciprocity, Langlands enunciated a reciprocity conjecture asserting that any complex Galois representation is automorphic. Around 1980, Langlands established certain cyclic base change and proved his reciprocity conjecture for 2-dimensional Galois representations with projective image isomorphic to $A_4$. In this talk, we will try to give a motivation of the Langlands reciprocity conjecture and discuss its relation to base change. If time permits, we will explain how the conjectural base change leads to Langlands reciprocity for all 3-dimensional Galois representations with solvable image.

This is a joint work with M. Ram Murty and V. Kumar Murty

Thursday, November 16, 3:30 p.m. Jeffery 222

Seminar in Free Probability and Random Matrices

Speaker: Pei-Lun Tseng

Title: Free independence of type B

Abstract: We will continue our discussion of type B R-transform. Then we are going to introduce the free independence of type B, and establish the relation between type B freeness and vanishing mixed cumulants in type B.

Seminar website: www.mast.queensu.ca/~mingo/seminar/

Friday, November 17, 2:30 p.m. Jeffery 234 - Department Colloquium

Title: The convexifying effect of Minkowski summation

Abstract: For a compact subset A of R^d, let A(k) be the Minkowski sum of k copies of A, scaled by 1/k. By a 1969 theorem of Emerson, Folkmann, Greenleaf, Shapley and Starr, A(k) approaches the convex hull of A in Hausdorff distance as k goes to infinity; this fact has important applications in a number of areas including mathematical economics. A few years ago, the speaker conjectured that the volume of A(k) is non-decreasing in k, or in other words, that when the volume deficit between the convex hull of A and A(k) goes to 0, it actually does so monotonically. While this conjecture holds true in dimension 1 (as independently observed by F. Barthe), we show that it fails in dimension 12 or greater. Then we consider whether one can have monotonicity of convergence of when non-convexity is measured in alternate ways. Our main positive result is that Schneider’s index of non-convexity of A(k) converges monotonically to 0 as k increases; even the convergence does not seem to have been known before. As a by-product, we also obtain optimal rates of convergence. We also obtain analogous results for the Hausdorff distance to the convex hull, as well as for the inner radius, and demonstrate applications to discrepancy theory. Joint work with Matthieu Fradelizi (Marne-la-Vallée), Arnaud Marsiglietti (CalTech), and Artem Zvavitch (Kent State).

Monday, November 20, 4:30 p.m. Jeffery 118 - Special Colloquium

Speaker: Alex Wright

Title: Dynamics, geometry, and the moduli space of Riemann surfaces

Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel.

Wednesday, November 22, 3:30 p.m. Jeffery 234 - Special Colloquium

Speaker: Jenny Wilson

Title: Stability in ordered configuration spaces

Abstract: The ordered configuration space F_k(M) of a manifold M is the space of ordered k-tuples of distinct points in M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which these spaces stabilize. In this talk, I will explain these stability patterns, and describe higher-order stability phenomena established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.

### Contact Info

 Department of Math & Stats Jeffery Hall, 48 University Ave. Kingston, ON Canada, K7L 3N6 Phone: (613) 533-2390 Fax: (613) 533-2964 mathstat@mast.queensu.ca Office Hours: 8:30am-12:00pm & 1:00pm-4:30pm