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2022 Lorne Campbell Lecture Series

Wednesday, December 7th, 2022

Time: 4:00 p.m.  Place: Stirling Hall A, or Online via Zoom (contact Abdol-Reza Mansouri for Zoom link)

Speaker: Moon Duchin (Tufts University)

Title: How Societies Choose

Abstract: How can we measure a healthy democracy? There are infinitely many election systems -- how voters fill out a ballot and then how we combine ballots to decide the outcome -- and they all have different properties and tendencies. I will give some philosophical and some mathematical perspectives on finding fairness in representative democracy.

Dr. Duchin is a mathematics professor at Tufts University and founder of the Metric Geometry and Gerrymandering group, a nonpartisan research group coordinating and publicizing research on geometry, computing, and their application to the redistricting process in the US. Her mathematical research concerns geometric topology, geometric group theory, Teichmuller theory, and the geometry of politics. Dr. Duchin is a fellow of the American Mathematical Society, gave a 2016 Mathematical Association of America distinguished lecture, was awarded a Guggenheim fellowship in 2018, and in 2018- 2019 was a fellow at the Radcliffe Institute for Advanced Study at Harvard.

Curves Seminar

Wednesday, November 30th, 2022

Time: 1:00 p.m.  Place: Jeffery Hall, Room 222

Speaker: Sonja Ruzic

Title: Localization Review, and Projective Toric Varieties

Abstract: We will give a brief review of localization. Afterwards, we will start the discussion of projective toric varieties.

Math & Stats Department Colloquium

Friday, November 25th, 2022

Time: 2:30 p.m.  Place: Jeffery Hall, Room 234

Speaker: Jean Pierre Mutanguha (IAS)

Title: Finding relative immersions of free groups

Abstract: Given an injective endomorphism of a free group, what is the "best" way to represent it so as to read off its dynamical properties? For automorphisms, the prevailing answer since the 1990s has been train tracks and their variations. In this talk, I answer this question for nonsurjective endomorphisms. To some degree, it turns out nonsurjectivity greatly simplifies matters --- a result that I found rather surprising. I proved that all injective endomorphisms can be uniquely represented by certain kinds of expanding immersions on graphs; a bit paradoxically, this representation is trivial when the endomorphism is an automorphism.

Math & Stats Department Colloquium

Friday, December 2nd, 2022

Time: 2:30 p.m.  Place: Jeffery Hall, Room 234

Speaker: Annette Karrer (McGill University)

Title: From Stalling’s Theorem to Morse boundaries

Abstract: Every finitely generated group G has an associated topological space, called a Morse boundary. It was introduced by a combination of Cordes and Charney{Sultan and captures the hyperbolic-like behavior of G at innity. In this talk, I will motivate the research on Morse boundaries in several steps. First, I will explain Stalling's theorem { a fundamental theorem in geometric group theory. Afterward, I will explain an analogous statement for so-called Gromov boundaries of Gromov-hyperbolic groups. As Morse boundaries generalize Gromov boundaries, this raises the question as to whether one can generalize this statement to Morse boundaries. Finally, we will see the relationship between a result on Morse boundaries of graphs of groups and this problem. Results presented are joint with Elia Fioravanti.

Dr. Karrer is a postdoc at McGill University, working in geometric group theory. After earning her PhD from Karlsruher Institute fur Tehcnoloqie under the advisement of Petra Schwer and Tobias Hartnick, and before her current position, Dr. Karrer worked as a postdoctoral fellow at the Technion in Israel.

Number Theory Seminar

Tuesday, November 29th, 2022

Time: 2:00 p.m.  Place: Jeffery Hall, Room 422

Speaker: Nic Fellini (���ϳԹ���Դ)

Title: A graph theoretic inequality and it's applications

Abstract: In this talk I will provide a graph theoretic approach to developing a simple sieve. We will see as an application how one can derive a multidimensional generalization of the Turán–Kubilius inequality. Time permitting, various other application will be discussed.

Curves Seminar

Wednesday, November 23rd, 2022

Time: 1:00 p.m.  Place: Jeffery Hall, Room 222 or Zoom

Speaker: Alexandre (Sasha) Zotine

Title: Toric Morphisms and Projective Geometry

Abstract: We will finish off our discussion of affine toric varieties by discussing torus equivariant maps. Afterwards, we will establish the foundations for studying projective toric varieties.

Number Theory Seminar

Tuesday, November 15th, 2022

Time: 2:00 p.m.  Place: Jeffery Hall, Room 422

Speaker: Francesco Cellarosi (���ϳԹ���Դ)

Title: The dynamical generalization of the Prime Number Theorem by Bergelson and Richter (Part 2)

Abstract: In a series of two talks, I will illustrate some of the results from the recent papers “Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative semigroup actions” by V. Bergelson and F.K. Richter (Duke Math. J. 171(15): 3133-3200, October 2022) and “A new elementary proof of the Prime Number Theorem” by F.K. Richter (Bulletin of the London Math. Society. 53(5): 1365-1375, October 2021).

In the first talk, I will assume several results to give a proof of a generalization of the PNT. The key idea will be to replace the average of an arithmetic function by a double average. This will prove a uniform distribution for the sequence (T^\Omega(n)x)_{n\geq1}, where T is a uniquely ergodic transformation of a compact metric space X, x is a point in X, and \Omega(n) the number of prime factors of n (counted with multiplicity). A particular choice of X, T, and x will yield the classical PNT.

In the second talk, I will get into the proofs of the results used in the first talk. We will see that, in the proof of a key lemma, we could either use the PNT or a weaker form of the PNT. The latter choice yields a novel elementary proof of the PNT, along with several generalizations thereof (e.g. the PNT along arithmetic progressions).

Algebra & Geometry Seminar

Monday, November 28th, 2022

Time: 4:30 p.m.  Place: TBA

Speaker: Sasha Pevzner (University of Minnesota)

Title: Symmetric Group Fixed Quotients of Polynomial Rings

Abstract:

Website details here: https://mast.queensu.ca/~georep/Fall%20'22.html

Number Theory Seminar

Tuesday, November 22nd, 2022

Time: 2:00 p.m.  Place: Jeffery Hall, Room 422

Speaker: M. Ram Murty (Queen's University)

Title: FERMAT QUOTIENTS AND CLASS NUMBERS OF REAL QUADRATIC FIELDS

Abstract: A famous conjecture of Ankeny, Artin and Chowla relates the class number of a real quadatic field with its fundamental unit. We will show that there are further connections with Fermat quotients and Wieferich style congruences. This is joint work in progress with Nic Fellini.

Curves Seminar

Wednesday, November 9th, 2022

Time: 1:00 p.m.  Place: Jeffery Hall, Room 222 or Zoom

Speaker: Alexandre (Sasha) Zotine

Title: Integral Closure and Normal Varieties

Abstract: We will digress from the toric setting to review the comcept of normality in algebraic geometry. Then we will return to the toric setting to see how this property can be identified combinatorially.