Date
Wednesday November 16, 2022Location
Jeffery Hall, Room 222 or ZoomWednesday, November 16th, 2022
Time: 1:00 p.m. Place: Jeffery Hall, Room 222 or Zoom
Speaker: Deepanshu Prasad
Title: Smooth Affine Toric Varieties
Abstract: We will look at smooth affine toric varieties and review the necessary material in order to do so.
Date
Friday November 18, 2022Location
Jeffery Hall, Room 422Friday, November 18th, 2022
Time: 10:00 a.m. Place: Jeffery Hall, Room 422
Speaker: Neil MacVicar (Queen's University)
Title: Computing Radix Expansions for Fractions of Gaussian Integers
Abstract: It is known that complex numbers can be written in base Gaussian integer b under conditions on both b and the coefficients of the powers of b (Katai and Szabo, 74). A representation of this kind is called a radix expansion. As per usual around these parts, the proof of the existence of an object does not always coincide with the object's construction - assuming the latter is even possible.
I will present an algorithm (Gilbert, 96) for determining the radix expansions of complex numbers whose real and imaginary parts are rational. Both the key and dynamical tie-in is that we want to leverage the iterated function system whose attractor is the set of expansions of negative powers of the base b.
Date
Friday November 18, 2022Location
Jeffery Hall, Room 234Friday, November 18th, 2022
Time: 2:30 p.m. Place: Jeffery Hall, Room 234
Speaker: Anush Tserunyan (McGill University)
Title: A backward look at pointwise ergodic theorems
Abstract: Pointwise ergodic theorems provide a bridge between the global behaviour of the dynamical system and the local combinatorial statistics of the system at a point. Such theorems have been proven in di erent contexts, but typically for actions of (semi)groups on a probability space. Dating back to Birkho (1931), the rst known pointwise ergodic theorem states that for a measure-preserving ergodic (typically many-to-one) transformation T on a probability space, the mean of a function (its global average) is approximated by local averages at almost every point x over the sets fx, Tx, ..., Tnxg, intervals of T-future of x. Almost a century later, we turn Birkho 's theorem backward, showing that the averages over trees of possible T-pasts also approximate the global average. This backward theorem for a single transformation surprisingly has applications to actions of free groups, yielding qualitatively new kinds of ergodic theorems for them. This is joint work with Jenna Zomback.
Dr. Tserunyan is an Assistant Professor in the Mathematics and Statistics Department at McGill University, and is a member of the Analysis lab at Centre de Recherches Mathematiques and of the Geometric Group Theory research group at McGill. Before this she was an Assistant Professor at the University of Illinois Urbana-Champaign. Dr. Tserunyan earned her PhD from the University of California Los Angeles under the advisement of Alexander S. Kechris (Caltech) and Itay Neeman (UCLA). She has held NSERC and NSF grants and has been a visiting fellow at the Bernoulli Center in Lausanne, Switzerland and the Institute Mittag-Leer in Djursholm, Sweden. Dr. Tserunyan is an editor for the Mathematical Logic Quaterly and the Archive for Mathematical Logic.
Rooted in logic and descriptive set theory, Tserunyan's research lies in the nexus of ergodic theory, measured group theory, countable Borel equivalence relations, and graph combinatorics.
Date
Tuesday November 8, 2022Location
Jeffery Hall, Room 422Tuesday, November 8th, 2022
Time: 2:00 p.m. Place: Jeffery Hall, Room 422
Speaker: Francesco Cellarosi (黑料吃瓜资源)
Title: The dynamical generalization of the Prime Number Theorem by Bergelson and Richter
Abstract: In a series of two talks, I will illustrate some of the results from the recent papers 鈥淒ynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative semigroup actions鈥 by V. Bergelson and F.K. Richter (Duke Math. J. 171(15): 3133-3200, October 2022) and 鈥淎 new elementary proof of the Prime Number Theorem鈥 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).
Date
Tuesday November 1, 2022Location
Jeffery Hall, Room 422Tuesday, November 1st, 2022
Time: 2:00 p.m. Place: Jeffery Hall, Room 422
Speaker: Ed Belk (Algebraic Capital Inc.)
Title: The local trace formula as a motivic identity.
Abstract: We consider a generalization of Parseval's identity, and show how model theory can be used to "transfer" this result from the known case of characteristic zero, to the new case of large positive characteristic.
Date
Friday November 11, 2022Location
Jeffery Hall, Room 422Friday, November 11th, 2022
Time: 10:00 a.m. Place: Jeffery Hall, Room 422
Speaker: Federico Salmoiraghi (Queen's University)
Title: From Morse homology to Floer theory
Abstract: In the first part of the talk we use classic Morse theory to show the existence of an Heegaard splitting for every closed 3-manifolds. In the second part we describe Witten鈥檚 approach to Morse homology and how this led to Floer theory. If time permits, we define the Heegaard Floer complexes, explaining how they arise as a special case of Lagrangian Floer theory.
Date
Monday November 14, 2022Location
TBAMonday, November 14th, 2022
Time: 4:30 p.m. Place: TBA
Speaker: Yvan Saint-Aubin (Universite de Montreal)
Title: Spin chains as a module over the affine Temperley-Lieb algebra
Abstract:
Website details here: https://mast.queensu.ca/~georep/Fall%20'22.html
Date
Wednesday November 2, 2022Location
Jeffery Hall, Room 222 or ZoomWednesday, November 2nd, 2022
Time: 1:00 p.m. Place: Jeffery Hall, Room 222 or Zoom
Speaker: Deepanshu Prasad
Title: Points of Affine Toric Varieties
Abstract: We will look at different ways to describe the points of affine toric varieties and try to understand when the points remain fixed under the action of the torus.
Date
Friday November 11, 2022Location
Jeffery Hall, Room 234Friday, November 11th, 2022
Time: 2:30 p.m. Place: Jeffery Hall, Room 234
Speaker: Zachary Selk (Queen's University)
Title: The Small Noise Limit of the Most Likely Element is the Most Likely Element in the Small Noise Limit
Abstract: In this talk, I discuss the Onsager-Machlup function and its relationship with the Freidlin-Wentzell rate function from large deviations. The Onsager-Machlup function can serve as a probability density on infinite dimensional spaces, where a uniform measure does not exist, and has been seen as the Lagrangian for the "most likely element". The Freidlin-Wentzell rate function is the large deviations rate function for small-noise limits and has also been identified as a Lagrangian for the "most likely element". This leads to a conundrum - what is the relationship between these two functionals?
We show that the small noise limit of the Onsager-Machlup functional both pointwise and in the sense of minimizers converges to the Freidlin-Wentzell functional for measures equivalent to arbitrary Gaussian measures. That is, we show that the small-noise limit of the most likely element is the most likely element in the small noise limit for infinite dimensional measures that are equivalent to a Gaussian. Examples of measures include the law of solutions to stochastic differential equations or the law of an infinite system of random algebraic equations.
Joint work with Harsha Honnappa
Date
Friday November 4, 2022Location
Jeffery Hall, Room 422Friday, November 4th, 2022
Time: 10:00 a.m. Place: Jeffery Hall, Room 422
Speaker: Federico Salmoiraghi (Queen's University)
Title: Floer theory and 3-dimensional topology
Abstract: Floer theory has drastically advanced our understanding of topology in dimension 3 and 4. In this talk we give an introduction to Morse homology and Lagrangian-Floer theory. The goal is to set the framework necessary to introduce Heegaard-Floer invariants and to describe some applications in low dimensional topology.
