## Topological Data Analysis - Gregory G. Smith (Queen's University)

### Monday, November 4th, 2019

**Time:** 2:30 p.m. **Place:** Goodes Hall 120

**Speaker:** Gregory G. Smith (Queen's University)

**Topics:** Homology over fields

All are welcome!

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**Time:** 2:30 p.m. **Place:** Goodes Hall 120

**Speaker:** Gregory G. Smith (Queen's University)

**Topics:** Homology over fields

All are welcome!

**Time:** 10:30 a.m** Place:** Jeffery Hall 319

**Speaker:** Giulio Tiozzo (Queen's University)

**Title:** Entropy and drift for Gibbs measures on geometrically finite manifolds.

**Abstract:** The boundary of a simply connected, negatively curved manifold carries two natural types of measures: on one hand, Gibbs measures such as the Patterson-Sullivan measure and the SRB measure. On the other hand, harmonic measures arising from random walks. We prove that the absolute continuity between a harmonic measure and a Gibbs measure is equivalent to a relation between entropy, drift and critical exponent, extending the previous formulas of Guivarc’h, Ledrappier, and Blachere-Haissinsky-Mathieu. This shows that if the manifold (or more generally, a CAT(-1) space) is geometrically finite but not convex cocompact, harmonic measures are singular with respect to Gibbs measures.

**Time:** 2:30 p.m. **Place:** Jeffery Hall 234

**Speaker:** Atabey Kaygun (Istanbul Technical University)

**Title:** Noncommutative Geometry for Fun and Profit.

**Abstract: ** There are whole fields of mathematics devoted to transferring problems of geometry and topology to commutative algebra (and vice versa) and solving them. This practice produced different "dictionaries'" of terms that tell us which type of objects in the realm of geometry or topology correspond to which other types of objects in the realm of algebra. In this talk, I am going to describe such a dictionary from the perspective of a homological algebraist who forgoes commutativity "for fun and profit" going through K-theory, cyclic and Hochschild homology, Hopf algebras, and quantum groups.

**Prof. Atabey Kaygun** works on homological and homotopical algebra in the context of noncommutative geometry. He obtained his Ph.D. from The Ohio State University in 2005. He was a postdoctoral fellow at the University of Western Ontario, KMMF-Warsaw University, Max-Plank-Institut fur Mathematik and University of Buenos Aires before joining the faculty of Bahcesehir University in 2009. He has been an associate professor at the Istanbul Technical University since 2016. Prof. Kaygun is currently on sabbatical and visiting Queen's University.

**Time:** 4:30-5:30 p.m. **Place:** Jeffery Hall 422

**Speaker:** Arpita Kar (Queen's University)

**Title:** On the distribution of certain sums of Random multiplicative functions.

**Abstract:** In this talk, I will discuss a result of Adam Harper regarding sums of Rademacher multiplicative functions $f(n)$, over those $n \leq x$ with $k$ distinct prime factors where $k$ is a function of $x$. In particular, we will discuss the Martingale central limit theorem due to Mcleish, and see how it establishes Harper's result.

**Time:** 4:30-5:30 p.m ** Place:** Jeffery Hall 319

**Speaker:** Mike Roth (Queen's University)

**Title:** Betti tables for canonical curves of genus 5 and 6, II.

**Abstract:** We will finish the computation of the possible Betti tables of genus 5 curves.

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**Time:** 4:00-5:30 p.m ** Place:** Jeffery Hall 319

**Speaker:** Mike Roth (Queen's University)

**Title:** Betti tables for canonical curves of genus 5 and 6.

**Abstract:** We will work out the Betti tables for canonically embedded curves of genus 5, and as time permits, genus 6. We will also discuss the classical theorems of Petri and Enriques-Babbage, the ‘basepoint-free pencil trick’ (due to Castelnuovo), and the modern idea of the ‘Castelnovo-Mumford regularity of a sheaf.

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**Time:** 2:30 p.m. **Place:** Goodes Hall 120

**Speaker:** Alireza Farhangdoost

**Topics:** Isomap and Locally Linear Embedding

Previous attendance or knowledge will not be required. All are welcome!

**Time:** 2:30 p.m. **Place:** Jeffery Hall 234

**Speaker:** Jeremy Quastel (University of Toronto)

**Title:** The KPZ fixed point.

**Abstract: ** The one dimensional KPZ universality class contains random growth models, directed random polymers, stochastic Hamilton-Jacobi equations (e.g.~the eponymous Kardar--Parisi--Zhang equation). It is characterized by unusual scale of fluctuations, some of which appeared earlier in random matrix theory, and which depend on the initial data, the explanation being that on large scales everything approaches a special scaling invariant Markov process, the KPZ fixed point, which turns out to be a new type of integrable system, leading to unexpected connections between probability and dispersive partial differential equations.

**Prof. Jeremy Quastel** specializes in probability theory, stochastic processes and partial differential equations. He obtained is Ph.D.~from the Courant Institute at NYU. He was a postdoctoral fellow at the MSRI in Berkeley, then was a faculty at UC-Davis until he returned to Canada in 1998, where he is now a professor at the University of Toronto and the current chair of the Mathematics department.

Among his accolades, Prof. Quastel received a Sloan Fellowship in 1996, was an invited speaker at the ICM in 2010, gave the Current Developments in Mathematics 2011 and St. Flour 2012 lectures, and was a plenary speaker at the International Congress of Mathematical Physics in Aalborg 2012. He is a fellow of the Royal Society of Canada.

**Time:** 3:30 p.m** Place:** Jeffery Hall 319

**Speaker:** Heejoung Kim (University of Illinois, Urbana-Champaign)

**Title:** Algorithms detecting stability and Morseness for finitely generated groups.

**Abstract:** For a word-hyperbolic group G, the notion of quasiconvexity is independent on the choice of a generating set and a quasiconvex subgroup of G is quasi-isometrically embedded in G. Kapovich provided a partial algorithm which, on input a finite set S of G, halts if S generates a quasiconvex subgroup of G and runs forever otherwise. However, beyond word-hyperbolic groups, the notion of quasiconveixty is not as useful. For a finitely generated group, there are two recent generalizations of the notion of a quasiconvex subgroup of a word-hyperbolic group, a ``stable'' subgroup and a ``Morse'' subgroup. In this talk, we will discuss various detection and decidability algorithms for stability and Morseness of a finitely generated subgroup of mapping class groups, right-angled Artin groups, toral relatively hyperbolic groups.

**Time:** 4:30-5:30 p.m. **Place:** Jeffery Hall 422

**Speaker:** Brad Rodgers (Queen's University)

**Title:** Moments and pseudomoments of the Riemann zeta-function, pt. 2.

**Abstract:** In a previous talk we discussed moments of the Riemann zeta function and "pseudomoments", in which the zeta-function is replaced by a finite Dirichlet polynomial. In this second talk we will further discuss random multiplicative functions and a variant of conjecture of Helson, proved with averaging weights by Bondarenko, Heap, and Seip. I hope to reintroduce the fundamental notions, so that this talk can be followed by audience members who missed the previous talk.