AdIMOM

Adelaide Institute of Mediocre and Outstanding Mathematics

About us | Past Seminars | Conference

Homemade Seminars

2021

• The geometry of the visual cortex: Contact structures and Gabor expansions, Vasiliki Liontou (University of Toronto).
• Concepts in Chemical Symmetry, Peter Viereck (Princeton University).
• Why you should care about knot homology, Oscar Kivinen (University of Toronto).
• Surface group representations and AdS 3-manifolds, Nathaniel Sagman (Caltech).
• Finite Topological Spaces, Fedya Kogan (University of Toronto).
• Kloosterman sums and G_2, Kostya Tolmachov (Perimiter Institute and University of Toronto).
• Minimal subfield of elliptic curves of number fields, Samprit Ghosh (University of Toronto).
• A New Generation of Mechanical Heart Valves, Arpin Bhullar (University of British Columbia Okanagan, Heart Valve Performance Laboratory).
• The Decomposition Theorem, Tudor Pădurariu (MIT).
• Magic Mirrors: stereochemistry in organic synthesis, Yufei Wang (Institute of Chemical Research of Catalonia).

• Curvature in metric geometry and General Relativity, Clemens Sämann (University of Toronto).
• Motivic integration in real algebraic geometry, Jean-Baptitse Campesato (University of Toronto).
• Optimal Transport and curvature - A journey from France to Italy via Russia, Christian Ketterer (University of Toronto).
• Universality and randomness: the Gaussian and KPZ classes, Virginia Pedreira (University of Toronto).
• Witnessing the Elephant., Fedya Kogan (University of Toronto).
• Class group statistics: stability and instability, Artane Siad (University of Toronto).
• Invariant random subgroups, Ilya Gekhtman (University of Toronto).
• Topological semantics, Ahmee Marshall-Christensen (University of Toronto).
• The spectral rigidity of chaotic billiards, Martin Leguil (University of Toronto).

• Boxcounting and rigidity, Noah Arbesfeld (Imperial College London).
• The dynamics of protoplanetary disks and their influence on the formation of planetary systems, J.j. Zanazzi (Perimeter Institute and the University of Toronto).
• Dynkin diagrams and categorification, Kostya Tolmachov (Perimeter Institute and the University of Toronto).
• Circle Diffeomorphisms, Selim Ghazouani (University of Warwick).
• Quantum contextuality, Emily Tyhurst (University of Toronto).
• Cohomology of holomorphic symplectic manifolds., Nikon Kurnosov (University of Georgia).
• Mechanisms and simple biochemistry of the digestion system and its connection to the brain, Lisa Vasiljewa (University of Göttingen).
• Poisson structures on character varieties, fundamental groupoids of arcs on Riemann surfaces with cusps, Anastasia Matveeva (Higher School of Economics).
• Generalized Brauer-Siegel Theorem, Anup Dixit,.
• Sequences to surfaces, Aaron Fenyes.
• Mathematician: Artist or Politician, Pooya Honaryar.
• Voice Leading Analysis in Pitch Class Space, Peter Angelinos.
• Chiral algebras and factorization algebras, Emily Cliff (University of Illinois at Urbana-Champaign).

• p-adic groups and the Satake isomorphism, Stefan Dawydiak.
• Mathematics of juggling, Patrick Fraser.
• Quantum K-theory and quantum integrable systems, Petya Pushkar (Yale University).
• Reinforcement learning, Annik Carson.
• How to make a group to act on a space with not that big dimension, Justin Martel.
• Combinatorial species, Fedya Kogan.
• Estimating the density of rational points on subsets of the reals, Derya Ciray (University of Konstanz).
• Uniformization of G-bundles on curves, Joshua Wen (University of Illinois at Urbana–Champaign).
• Cohomology annihilators and chicken mcnuggets, Özgür Esentepe.
• Cohomogeneity-one Actions and a Little-remarked Structure on the Mayer-Vietoris Sequence, Jeffrey Carlson.
• The p-curvature Conjecture and Monodromy About Simple Closed Loops, Ananth Shankar (Harvard University).
• Variation of Faltings Heights of CM Abelian Varieties, Lucia Mocz (Princeton University).
• Poisson Geometry and Representation Theory, Sasha Shapiro.
• Modular Forms and Adeles, Max Klambauer.
• Feynman diagrams from inner products, Aaron Fenyes.
• Hives and the Saturation Conjecture , Ian Le (Perimeter Institute).
• The Hodge Theorem, Ethan Yale Jaffe (MIT).

2016

• The Moduli Space of Stable Curves and Its Intersection Theory, Jason van Zelm (University of Liverpool).
• Dynamics on Moduli Spaces, Eduard Duryev, (Harvard University).
• Cluster Algebras and Varieties and Their Applications, Fima Abrikosov (Yale University).
• Some compactifications in Lie theory, Peter Crooks.
• Gross' Proof of the Chowla-Selberg Formula, Payman Eskandari.
• Resolution of Singularities, Bernd Schober (Fields Institute).
• Math of Musical Scale, Fulgencio Lopez.
• Toric varieties, log Calabi-Yau's, and Combinatorial Representation Theory, Timothy Magee (University of Texas).
• Complex Reflection Groups, Duality Groups, such and such, Benjamin Briggs.
• Deformation Theory of Dirac Structures via L-infinity Algebras, Mykola Matviichuk.
• Geometric Invariant Theory, Elliot Cheung (University of British Columbia).
• Wonderful Compactification of Quantum Groups, Iordan Ganev (University of Texas at Austin).
• Laurence Sterne and The Reception of His Novels in Stalin's Russia in the 1930s, Peter Budrin (Literature Department at UofT).
• On Integrable Systems, Krishan Rajaratnam.
• Some Motivation for Geometric Representation Theory, Anne Dranovski.
• Virtual Cohomological Dimension and Borel-Serre Formula, Marvin Martel.
• Integrable Systems and Algebraic Geometry, Anton Izosimov.
• Some Motivation for Noncommutative Algebraic Geometry, Özgür Esentepe.
• Why Moduli Spaces? , Changho Han (Harvard University).

2015

• Knots, Links and 3-manifolds, Eduard Duryev (Harvard University).
• Borel-Weil-Bott Theorem and Weyl Character Formula, Petr Phuskar (Columbia University).
• Rational Homotopy Theory, Dylan Butson (Perimeter Institute).
• McKay Correspondence, Louis-Philippe Thibault.
• On Moduli Space of Algebraic Curves, Ivan Telpukhovskiy.
• Tait-Kneser Theorem, Leonid Monin.
• Taniyama-Shimura Conjecture, Gaurav Patil.
• q-Homotopy for Simplicial Complexes, Parker Glynn-Adey.
• Cyclic Homology, Vincent Gelinas.
• An Introduction to Derived Categories, Benjamin Briggs.
• Tropics and Gromov-Witten Invariants, Leonid Monin.
• Flat Surfaces, Leonid Monin.
• On Bernstein-Kouchnirenko Theorem, Leonid Monin.

Abstracts

Speaker:Vasiliki Liontou
Date:May 15, 2021
Title:The geometry of the visual cortex: Contact structures and Gabor expansions
Abstract:Since Hubel and Wiesel discovered the modular structure of the visual cortex, the part of our brain which is responsible for the interpretation of visual stimuli, the problem of a theoretical understanding of the experimental data on what is known as geometrical architecture of the visual brain, has emerged. The geometry of interest is not the anatomical geometry of the brain but the differential geometry of the connectivity between neural cells. The purpose of this talk is to present how the neurons of the visual cortex behave as a fiber bundle equipped with a contact structure as well as functions used in non-orthogonal series expansions of signals. Can these two models be combined to give interesting results for mathematicians and neuroscientists?

Speaker:Peter Viereck
Date:May 8, 2021
Title:Concepts in Chemical Symmetry
Abstract:Don't worry, this chemistry talk will have 0 (ok maybe 1 or 2 I can't help myself) molecular structures or even chemical names. Instead, I will focus on handwaving my way through a Chemist's use of Symmetry, and in particular the Chemist's superficial understanding and utility of Group Theory concepts. At the end, possibly after a standing ovation, I will discuss Asymmetry, and time permitting the field of Asymmetric Catalysis, which I have been pretending to study the past 4 years (with limited success).

Speaker:Oscar Kivinen
Date:April 24, 2021
Title:Why you should care about knot homology
Abstract: I will present some gentle and not-so-gentle mathematical motivation for knot invariants, in particular link homology theories. Time permitting, I will also try to give a more rigorous introduction.

Speaker:Nathaniel Sagman
Date:April 17, 2021
Title:Surface group representations and AdS 3-manifolds
Abstract: Associated to any (finite type) hyperbolic surface is the Teichmüller space of marked hyperbolic metrics on that surface. It turns out that this identifies with a special space of representations of the fundamental group into PSL(2,R) (mod conjugation). An aim of Higher Teichmüller theory is to associate more general "geometric structures" to certain representations into Lie groups. An Anti-de Sitter (AdS) 3-manifold is a Lorentzian 3-manifold of constant curvature -1. In this talk, we will discuss some recent results on AdS 3-manifolds that fit into the Higher Teichmüller framework.

Speaker:Fedya Kogan
Date:April 3, 2021
Title:Finite Topological Spaces
Abstract:I was initially interested in finite topological spaces for several reasons: - a characterization of spectra of commutative rings as limits of finite T_0-spaces - a testing ground for understanding convolution algebras - simple examples of non-Haudsdorff spaces Currently I can't really build a talk out of any of the three things above, so my plan is to explain the basics of homotopy theory of finite spaces and explain how this is applied to algebraic topology and finite group theory.

Speaker:Kostya Tolmachov
Date:March 27, 2021
Title:Kloosterman sums and G_2
Abstract:Kloosterman sums are a certain kind of trigonometric sums appearing in many problems of number theory. I will try to give a motivated exposition of some results of Deligne and Katz that say that probabilistic properties of these sums are governed by various Lie groups (including the exceptional Lie group G_2).

Speaker:Samprit Ghosh
Date:March 20, 2021
Title:Minimal subfield of elliptic curves of number fields
Abstract:The concept of minimal subfields of an elliptic curve defined over a number field was introduced by Murty and Akbary in 2001. This talk will be an exposition of their paper. Their work sits on the sweet intersection of Arithmetic geometry, Galois representation theory and L-functions. When I first read the paper I had little knowledge about those areas and yet the paper was very much accessible. So, I hope it will be the same for you.

Speaker:Arpin Bhullar
Date:March 6, 2021
Title:A New Generation of Mechanical Heart Valves
Abstract:Valvular heart disease is a cardiovascular condition characterized by damage to any number of the four valves within the human heart. As the disease progresses, the damage sustained can require the implantation of a prosthetic heart valve. One type of prosthetic valve is a mechanical heart valve, characterized by its near infinite lifespan and lifelong requirement of anticoagulation medication. We set out to design a new valve that addressed the inherent thrombogenicity of modern mechanical heart valves, eliminating the need for medication. The result was the Okanagan valve.

Speaker:Tudor Pădurariu
Date:February 27, 2021
Title: The Decomposition Theorem
Abstract:he decomposition theorem (of Beilinson-Bernstein-Deligne-Gabber) is a very important tool in algebraic geometry. I plan to mention some of the techniques used in the topology of algebraic varieties (such as perverse sheaves, Lefschetz theorems etc), and then to explain how the decomposition theorem helps in this study.

Speaker:Yufei Wang
Date:Feburary 20, 2021
Title:Magic mirrors: stereochemistry in organic synthesis
Abstract:In this talk, we will be a quick lesson on what organic chemistry is, what stereochemistry is and how it plays a role in natural products and biological systems.

Speaker: Clemens Sämann
Date: Saturday November 30, 2019
Title: Curvature in metric geometry and General Relativity
Abstract: I will review the notion of curvature in the setting of metric and semi-Riemannian geometry. Curvature is of fundamental importance in General Relativity (GR), where it relates the geometry with the matter-energy content of the space. Then I will describe some recent work which imports ideas and tools from metric geometry into GR, where it allows to treat spacetimes of low regularity (Lorentzian manifolds with a metric of regularity below C^{1,1}, i.e., the derivative exists and is locally Lipschitz continuous).

Speaker: Jean-Baptitse Campesato
Date: Saturday November 23, 2019
Title: Motivic integration in real algebraic geometry
Abstract: Several recent results in real algebraic and analytic geometries rely on arguments coming from motivic integration. These results concern blow-Nash maps, real singularities via the blow-analytic and the arc-analytic equivalences, and, more recently, inner-Lipschitz maps. Similarly to the complex case, the real motivic measure assigns a "volume" to some sets of real analytic arcs on a real algebraic variety. However, it is not possible to use the complex construction as it is because Chevalley's theorem and the Nullstellensatz do not hold in this real context. First I will explain the construction of this real motivic measure and how to process the cited above issues. Then I will focus on an application of this real motivic measure: an inverse mapping theorem for blow-Nash maps (i.e. semialgebraic maps which become real analytic after being composed with blowings-up). These maps recently played an important role in real algebraic geometry and in the classification of real singularities.

Speaker: Christian Ketterer
Date: Saturday November 16, 2019
Title: Optimal Transport and curvature - A journey from France to Italy via Russia
Abstract: In this talk I will give a crash course to the theory of optimal transport and explain its role in the synthetic characterization of lower Ricci curvature bounds.

Speaker: Virginia Pedreira
Date: Saturday November 9, 2019
Title: Universality and randomness: the Gaussian and KPZ classes.
Abstract: In this talk we will introduce the concept of universality from a probability point of view. We will try to explain what makes the Gaussian distribution universal, introduce the KPZ class and understand what makes it harder to prove universality in this class. The goal is to introduce most ideas, objects and techniques that will be discussed. Hopefully, the audience will be able to understand a couple more minutes in the next probability colloquium talk.

Speaker: Fedya Kogan
Date: Saturday October 19, 2019
Title: Witnessing the Elephant
Abstract: I will try to give an accessible introduction to Topos Theory. Topoi were initially defined by Grothendieck, while pursuing the notion of what is now known as etale cohomology, in order to generalize the notion of sheaves on a space. Soon after, Lawvere and Tierney noticed that topoi provide a suitable semantics, for a variety of logic systems, capable of replacing ZFC as a type-theory like foundation for mathematics. Together this results in topoi being a peculiar bridge between geometry and logic. I will try to illustrate the previous sentence by going over some topos theory basics, and then culminating in discussing independence results in set theory and the classifying topos of local rings.

Speaker: Artane Siad
Date: Saturday September 28, 2019
Title: Class group statistics: stability and instability.
Abstract: The Cohen-Lenstra conjectures describe the distribution of class groups and related statistics as one varies over the collection of all number fields through a “stacky counting” heuristic. We will examine the questions of stability and instability of a particular statistic, the average number of non-trivial 2-torsion elements in the class group (*), when one “perturbs” the collection of all number fields. The talk will begin with a gentle introduction to stacky counting and the Cohen-Lenstra heuristic. We will then discuss the stability of statistic (*) in the 2 cases where Cohen-Lenstra has been proven and present new insight on the instability of (*) under so called “global” perturbations.

Speaker: Ilya Gekhtman
Date: Saturday March 2, 2019
Title: Invariant random subgroups
Abstract: Let G be a locally compact group. An invariant random subgroup (IRS) of G is a conjugation invariant Borel probability measure on the space of closed subgroups of G. They arise as stabilizers of probability measure preserving actions, and are a natural generalization of both normal subgroups and lattices in G. Thus, many people have tried to extend results about lattices and normal subgroups in the context of IRS: for example, nontrivial invariant random subgroups in rank 1 Lie groups are discrete, geometrically dense, and have growth rate more than half of that of a cocompact lattice. The space IRS(G) of invariant random subgroups of G is a compact G-space, studying which can provide new insight into generic properties of lattices in G, for instance when G is a simple Lie group. When G=SL_2R the space of invariant random subgroups contains moduli spaces of all hyperbolizable Riemann surfaces, and the associated compactifications is related to the Deligne-Mumford compactification. I will talk about these things.

Speaker: Ahmee Marshall-Christensen
Date: Saturday February 23, 2019
Title: Topological semantics
Abstract: Though topological semantics were the first semantics given for modal logic, for much of the history of modal logic, they have often been ignored in favor of Kripke semantics. For many approaches to modal logic, however, the topological semantics furnish a much more exciting landscape. In fact, given that one is interested in modal logics with certain assumptions, the topological semantics are provably more rich. In particular, epistemic logic, philosophy of science, and quantified modal logic have all recently benefited from a topological perspective. I will introduce some common modal logics and motivate Kripke semantics with an epistemic logic puzzle demonstration. Then, we will prove a completeness result of everyone's favorite modal logic, S4. This result will be ported over to the topological world, where we can further prove some general results about logics of spaces. On the other hand, we will prove a specific result about Q, which, when coupled with the general results, will tell us that R, R^n, Cantor space, manifolds, CW-complexes, and probably some other stuff is all boring.

Speaker: Martin Leguil
Date: Saturday January 19, 2019
Title: The spectral rigidity of chaotic billiards
Abstract: The question of dynamical spectral rigidity has been investigated in a range of settings: for hyperbolic surfaces, convex domains with symmetries... In a joint work with Péter Bálint, Jacopo De Simoi and Vadim Kaloshin, we study a class of dispersing billiards on the plane obtained by removing strictly convex obstacles satisfying the non-eclipse condition. In this case, there is a natural labelling of periodic orbits, and we want to know how much geometric information can be recovered from the Marked Length Spectrum, i.e., the set of lengths of periodic orbits together with their labelling. In particular, we show that for each period two orbit, the curvature at the two bouncing points can be reconstructed. We also show that the Lyapunov exponent of each periodic orbit can be recovered. Our approach is based on a sequence of periodic orbits with symmetries which shadow more and more closely some orbit homoclinic to the periodic orbit that we want to describe. In the case of period two orbits, we will explain how it is possible to extract some asymmetric information to distinguish between the two points in the orbit.

Speaker: Noah Arbesfeld
Date: Saturday December 1, 2018
Title: Boxcounting and rigidity
Abstract: Just in time for the holidays, I'll give an overview of boxcounting approaches to localization computations arising in the study of Hilbert schemes of points on curves, surfaces, and threefolds; rigidity will be a recurring theme. In the holiday spirit, I only have enough material for 1 hour, but maybe it'll last us 8; time permitting, I'll conclude with some reading (tbd).

Speaker: J.j. Zanazzi
Date: Saturday November 16, 2018
Title: The dynamics of protoplanetary disks and their influence on the formation of planetary systems
Abstract: Before the discovery of planets outside our solar system, astronomers based our theories of how planets formed on the solar system planets. We predicted small rocky planets would form close to their host stars, while large gaseous planets would form far. The orbits of of the planets were expected to be circular, and orbit in the same direction as their host stars rotation. It came as a surprise to the astronomical community that the first planets discovered were massive planets on close-in or eccentric orbits orbiting in directions very different than their host star's rotation. In this talk, we will heuristically discuss the main ideas on how to form these strange planetary systems. We will also briefly mention the speaker's contribution to this field, looking at how gravitational interactions between disks of gas and dust orbiting young stars (protoplanetary disks) affect the planetary systems formed within these disks.

Speaker: Kostya Tolmachov
Date: Saturday November 10, 2018
Title: Dynkin diagrams and categorification
Abstract: I will talk about McKay correspondence and will present a paper by Etingof and Khovanov, in which several its generalizations are considered.

Speaker: Selim Ghazouani
Date: Saturday October 26, 2018
Title: Circle Diffeomorphisms
Abstract: I will explain basic properties of circle diffeomorphisms. In many cases they are surprisingly rigid.

Speaker: Emily Tyhurst
Date: Saturday October 13, 2018
Title: Quantum contextuality
Abstract: Quantum computing has been the source of much excitement in the last decade, promising exponential speed-up in computation of a handful of tricky problems. Though it is conjectured that the class of polynomial-time quantum-solvable problems (BQP) is larger than the class of polynomial-time classically solvable problems (P, BPP), it is not clear what resource properties of quantum computers quantify this speed-up. In this talk I will provide a summary of “contextuality”, a current contender for the essential quantum resource that allows for faster computation. Further, in [1806.04657] myself and my collaborators demonstrate a connection between algebraic topology and contextuality. I will lay out this framework within certain models of quantum computation, and prove a few results that are of interest to understanding contextuality as the quantum resource.

Speaker: Nikon Kurnosov
Date: Saturday October 6, 2018
Title: Cohomology of holomorphic symplectic manifolds
Abstract: I will talk about compact holomorphic symplectic manifolds, mostly with focus on the Kahler case. Cohomology algebra of hyperkahler manifolds is Frobenius algebra and the total Lie algebra of Lefschetz sl(2)-triples acting on it is so(4,b_2-2) by results of Loojenga-Lunts and Verbitsky. I will discuss restrictions on Betti numbers, Kuga-Satake construction, deformation theory, and existence of Beauville-Bogomolov-Fujiki form.

Speaker: Lisa Vasiljewa
Date: Wednesday September 26, 2018
Title: Mechanisms and simple biochemistry of the digestion system and its connection to the brain
Abstract: In this short talk I will focus on a simple explanation of the mechanics and biochemistry behind the digestion system’s processes and its regulation. I will try to make clear the hormone feedback cycles in our digestion, discuss the nature of feeling hunger as well as the interaction between the brain and the stomach, also known as the "brain-gut axis".

Speaker: Anastasia Matveeva
Date: Sunday July 15, 2018
Title: Poisson structures on character varieties, Fundamental groupoids of arcs on Riemann surfaces with cusps
Abstract: No special knowledge is required!

Speaker: Anup Dixit
Date: Saturday March 31, 2018
Title: Generalized Brauer-Siegel Theorem
Abstract: For a number field K/Q, the class number h_K captures how far the ring of integers of K is from being a PID. The study of class numbers is a theme in number theory. In order to understand how the class number varies upon varying the number field, Siegel showed that the class number times the regulator tends to infinity in any sequence of quadratic number fields. Brauer extended this result to sequence of Galois extensions over Q. This is the Brauer-Siegel theorem. Recently, Tsfasman and Vladut conjectured a Brauer-Siegel statement for asymptotically exact sequence of number fields. In this talk, we prove the classical Brauer-Siegel and the generalized version in several unknown cases. We also provide some effective versions of Brauer-Siegel in the classical setting.

Speaker: Aaron Fenyes
Date: March 24th, 2018
Title: Sequences to surfaces
Abstract: When you write the fractional part of a number as a decimal, you're turning a point on the circle R/Z into an infinite sequence of digits—a geometric object into a dynamical one. This kind of passage from smooth geometry to discrete dynamics leads to some weird and wonderful descriptions of two-dimensional surfaces. By the end of this talk, I hope I'll convince you that hyperbolic surfaces are flat surfaces, flat surfaces are sequence spaces, and even the simplest sequence spaces are full of geometric surprises.

Speaker:Pooya Honaryar
Date:Feb 17th, 2018
Title: Mathematician: Artist or Politician:
Abstract: What happens when a mathematician, decides to talk about life and other important things such as love, philosophy, sociology, politics and literature? I believe the outcome would be interesting for other mathematicians as well! First I try to address these 2 questions: why a person decides to become a mathematician?(who was Unabomber? Is there a difference between Hardy’s and Thurston’s way of Masaining(doing math!)) why so many math phd’s become statistician and economists?(stat from math geneology project- why they don’t become politicians instead(Cedric Villani + Angela Merkel = ??)). I also have a theory, which is kind of the reason “I” ‘m (or am not going to) doing (do) math (anymore). This theory is pretty much rooted in my background as an eastern person, born in the specific time and location, and to a specific family. I think it would be a bit understandable for the people with knowledge about the eastern culture. In this theory I want to show how on one hand the government tries to make “screws” for his machine and on the other hand, large companies try to make their own “screws” and how no one cares for the beauty of twisting anymore. I arrive at a triangle, on one vertex are engineers, on the other two politicians and artists. And one of my main theses is to show how close the last two are to each other. If time allows, I use this theory of mine and apply it to the actual crisis that we have in our department and arrive at a solution.

Speaker: Peter Angelinos
Date: Feb 10, 2018
Title: Voice Leading Analysis in Pitch Class Space
Abstract: Although music is several thousands of years old as a cross-cultural phenomenon, it was only recently that Dmitri Tymoczko formulated his theory of the continuous geometry of pitch class space. We will discuss the precursors to this theory (i.e. discrete pitch lattices such as Euler's Tonnetz) and how Tymoczko addresses their shortcomings. Time permitting, we will introduce other structures on Tymoczko spaces (such as submajorization partial orders) and analyze their use in music theory.

Speaker: Emily Cliff
Date: January 26, 2018
Title: ​C​hiral algebras and factorization algebras
Abstract: The definition of a vertex algebra was formulated by Borcherds in the 1980s to solve algebraic problems, but these objects turn out to have important applications in mathematical physics, especially related to models of 2d conformal field theory. In the 1990s, Beilinson and Drinfeld gave geometric formulations of the definition, which they called chiral algebras and factorization algebras. These different approaches each have advantages and disadvantages: for example, the definition of a vertex algebra is more concrete and has so far been better studied; on the other hand, the geometric approach of chiral algebras and factorization algebras allows for transfer of knowledge between the fields of geometry, physics, and representation theory, and furthermore admits natural generalizations to higher dimensions. In this talk we will introduce all three of these objects; then we will discuss the relationships between them, especially focusing on how information from any one approach can lead to new understanding in the others. ​

Speaker: Stefan Dawydiak
Date: December 2, 2017
Title: p-adic groups and the Satake isomorphism
Abstract: We will start by introducing a hopefully nice way to think about locally profinite groups, and then introduce an important algebra of functions on them: the (spherical) Hecke algebra. We'll then give some ideas behind the Satake isomorphism, a result that relates the Hecke algebra of G with representations of the Langlands dual of G. We'll conclude by saying how this brings Kazhdan-Lusztig polynomials into the picture, and what happens when q=1.

Speaker: Patrick Fraser
Date: November 18, 2017
Title: Mathematics of juggling
Abstract: Perhaps juggling is not the first application to come to mind when one thinks of discrete mathematics however, there are many fascinating connections between mathematics and this unorthodox art form. In this talk, we will explore the challenge of rigorously describing juggling patterns and interesting structures that arise as a result such as graphs, braids, and Weyl groups.

Speaker: Petya Pushkar
Date: November 4, 2018
Title: Quantum K-theory and quantum integrable systems
Abstract: In this talk I will define the quantum K-theory of Nakajima quiver varieties and show its connection to representation theory of quantum groups and quantum integrable systems on the examples of the Grassmannian and the flag variety. In particular, the Baxter operator will be identified with operators of quantum multiplication by quantum tautological classes via Bethe equations. Quantum tautological classes will also be constructed and, time permitting, an explicit universal combinatorial formula for them will be shown. Based on joint works with P.Koroteev, A.Smirnov and A.Zeitlin

Speaker: Emily Cliff
Date: October 22, 2017
Title: Reinforcement Learning
Abstract: Reinforcement learning (RL) is an area of machine learning concerned with optimal behavioural control. RL provides a normative framework in which to understand how the brain can learn to make decisions for maximizing subjective reward in the absence of an explicit teaching signal. Currently, even agents using state-of-the-art control systems in RL tasks are data inefficient and challenged by nonstationary environmental conditions, including changes in statistics of reward probability and transitions between states, which biological agents handle with relative ease. It has been proposed that storing information about experienced episodes in a memory cache -- modeled after the activity of the hippocampus in animals -- can help bootstrap learning in RL systems to improve the speed of learning and ability to cope with nonstationary environments. My research proposes three different representations for episodic memories stored in such a system and aims to resolve which provides the greatest benefit to RL systems when used in conjunction with a standard controller. Furthermore I aim to resolve how these representations can account for features of animal behaviour, and which of these representations -- if any -- are likely to explain how episodic memory is represented in the hippocampus.

Speaker: Justin Martel
Date: September 30, 2017
Title: How to make a group to act on a space with not that big dimension
Abstract: We describe homological-duality on manifolds-with-corners $(X, \del X)$, where $X$ is a contractible space supporting a free $G$-action, with $G$ a finitely-generated discrete matrix group.
Effectively computing $G$-equivariant (co)homology on $X$ is expensive process, which is burdened by the fact that (!): the apparent space dimension $dim[X]$ is typically much larger than the algebraic symmetry dimension $vcd[G]$ of the symmetry group $G$. This observation originates with Borel-Serre from ~1980s in their paper, and leads to interesting ideas.
Our goal is to describe explicit $G$-equivariant subvarieties $Z$ of $X$, whose topological dimension coincides with the symmetry dimension. We display the subvarieties $Z$ as ``Kantorovich Singularities" of an optimal semicoupling measure, with respect to a (gated)-electron-cost. The Kantorovich duality principle underyling mass transport methods is, we claim, the fundamental fact responsible for poincare duality. Attendees can expect details!

Speaker: Fedya Kogan
Date: September 16, 2017
Title: Combinatorial species
Abstract: Tired of doing enumerative combinatorics by using shady operations on generating series? Try a fresh conceptual method for counting graphs and much more! This technique was developed by a king of categories Andre Joyal; the idea is quite abstract, but essentially very accessible. This talk will be challenging, yet simple, and most importantly fun!

Speaker: Derya Ciray
Date: June 27, 2017
Title: Estimating the density of rational points on subsets of the reals
Abstract: This talk is about a method used to estimate the density of rational points (of bounded height) on subsets of the reals. A set has a mild parametrization, if it can be covered by a finite number of smooth functions with certain bounds on their derivatives (mild functions). I will explain how mild parametrization is used to achieve 'good bounds' on the density of rational points for certain sets.

Joshua Wen:
Date: June 04, 2017
Title: Uniformization of G-bundles on curves
Abstract: To construct and classify G-bundles on the projective line, one can cut the line into two disks and use an element of the loop group to glue trivial bundles on each disk. By accounting for automorphisms of the bundles on each disk, we get a presentation of moduli of G-bundles on the line in terms of double cosets of the loop group. Surprisingly, a similar double coset construction exists for moduli of G-bundles on any compact Riemann surface---this is the content of the uniformization theorems of Beauville-Laszlo and Laszlo-Sorger. These presentations allow one to relate certain 'strange' induced representations of the loop group to vector bundles on the moduli spaces, which leads to the study of conformal blocks.

Speaker: Özgür Esentepe
Date: March 18, 2017
Title: Cohomology annihilators and chicken mcnuggets
Abstract: A very nice theorem due to Serre states that a ring is regular (read smooth) if and only if it there is a finite number d such that for all n bigger than d and for all modules M and N, we have Ext^n(M,N)=0. This is equivalent to saying that any element inside the ring annihilates all large extension groups between any two modules. When the ring is not regular, the elements which annihilate all large extension groups form a nontrivial ideal. I will talk about this ideal, what happens in dimension one and how the answer was motivated by the coin problem (aka chicken mcnugget problem).

Speaker: Jeffrey Carlson
Date: March 11, 2017
Title: Cohomogeneity-one actions and a little-remarked structure on the Mayer-Vietoris sequence
Abstract: The action of a Lie group G on a manifold M is said to be of cohomogeneity one if the orbit space M/G is a 1-manifold; such actions are arguably the simplest after the transitive, and accordingly have been long discussed and also classified in low dimensions. In this talk, we compute the equivariant K-theory and Borel equivariant cohomology rings $K^*_G M$ and $H^*_G(M;\mathbb Q)$ of such actions. The proof follows readily from a result of potentially much wider interest, namely the existence of an additional algebraic structure on the Mayer-Vietoris sequence for any multiplicative cohomology theory which, though easily stated and simply demonstrated, has-as best we can tell-nevertheless escaped mention in introductory topology texts. This work is joint with Oliver Goertsches, Chen He, and Augustin-Liviu Mare.

Speaker: Ananth Shankar
Date: March 4, 2017
Title: The p-curvature Conjecture and Monodromy About Simple Closed Loops
Abstract: We will discuss vector bundles with flat connections, and talk about algebraic criteria for the existence of a full set of flat sections.

Speaker: Lucia Mocz
Date: February 10, 2017
Title: Variation of Faltings Heights of CM Abelian Varieties
Abstract: We discuss a proof of a new Northcott property for Faltings' heights of CM abelian varieties. In particular, we show that there are finitely many CM abelian varieties of a fixed dimension of bounded Faltings height. We will focus this talk on understanding the variation of Faltings heights for CM abelian varieties within isogeny classes, with a full discussion on the explicit local (intersection) computations.

Speaker: Sasha Shapiro
Date: February 4, 2017
Title: Poisson Geometry and Representation Theory
Abstract: I will outline relations between Poisson geometry and representation theory. In particular, I will explain how the universal enveloping algebras of simple Lie algebras on one hand and the quantum groups on the other arise in the same Poisson geometric framework, and why differential and q-difference operators are so important in their representation theory.

Speaker: Max Klambauer
Date: January 28, 2017
Title: Modular Forms and Adeles
Abstract: Modular forms are the prototypical example of an automorphic form, though you wouldn't know that from the definitions. By the end of the talk we shall see how a modular form, defined in a straightforward way on the complex upper half plane, can be viewed as an automorphic form, which lives on the more complicated adeles. We will begin by talking about modular forms (just for the sake of it), then move on to talk about Tate's groundbreaking thesis to get a hang for the adeles. After this we will march on to our goal.

Speaker: Aaron Fenyes
Date: January 21, 2017
Title: Feynman diagrams from inner products
Abstract: Last Saturday, the audience complained when the speaker recalled a little undergraduate linear algebra, so this Saturday I'll give a talk consisting entirely of undergraduate linear algebra. I'll show you how fancy-sounding gadgets from quantum field theory, like Feynman diagrams and Wick's theorem, arise naturally from the linear algebra of polynomials on an inner product space.
The main part of the talk will follow the attached notes, though I'll skip most of the background and cut right to the chase. With luck, I'll also manage to prepare a few interesting examples.

Speaker: Ian Le
Date: January 14, 2017
Title: Hives and the Saturation Conjecture
Abstract: I will start by introducing some of the basics of the finite-dimensional representation theory of GL_n. I will then define Littllewood-Richardson coefficients, and talk about the problem of computing them. The saturation conjecture is a very interesting conjecture about Littlewood-Richardson coefficients that tells us that in some ways they behave regularly. I will explain how hives were used to solve the saturation conjecture, and also explain some relations of this problem to other areas of math.

Speaker: Ethan Yale Jaffe
Date: January 7, 2017
Title: The Hodge Theorem
Abstract: The Hodge Theorem is a beautiful theorem connecting the topology of a compact Riemannian manifold to its geometry. In this talk I will sketch a proof of the Hodge theorem using pseudodifferential operators and the techniques of (global) microlocal analysis.

Speaker: Jason van Zelm
Date: December 10, 2016
Title: The Moduli Space of Stable Curves and Its Intersection Theory
Abstract: In this talk I will introduce the moduli space of stable curves and its Chow ring. I will define a particularly nice subring of the Chow ring called the tautological ring and give a formula for the intersection of two classes in the tautological ring. Finally, I will discuss some recent developments about the limitations of this tautological subring.

Speaker: Eduard Duryev
Date: November 25, 2016
Title: Dynamics on Moduli Spaces
Abstract: - Every Riemann surface of genus 2 admits a non-constant holomorphic map to a Riemann sphere. But does it admit one to a given elliptic curve? Any elliptic curve?
- Take a bunch of unit squares in a complex plane and glue them along their opposite sides so that they form a closed surface. You will obtain a Riemann surface, a point in the moduli space of complex structures. Can you obtain any complex structure via such construction? What if you slightly generalize and start with a bunch of polygons instead of squares?
- Take your favorite matrix from SL(2,Z) and apply it to that bunch of unit squares in the plane remembering the identification you chose. What kind of surface do you get? Do you ever get the same thing? (spoiler: very often you do!)
These questions come from the area called 'dynamics on the moduli space’ or 'translation surfaces'. It allows another view on the moduli space of curves as polygons in the plane. There is an action of GL(2,R) on that space and there is a rich study of the orbits of that action as they provide subvarieties of M_g.

Speaker: Fima Abrikosov
Date: November 19, 2016
Title: Cluster Algebras and Varieties and Their Applications
Abstract: Cluster algebras were introduced by Fomin & Zelevinskiy in early 2000’s. Since then this subject became a striving area of research and many applications were found ‘in nature'. Brightest of them include theory of canonical bases for Lie algebras and categorical framework for the theory of Donaldson-Thomas invariants. I will give a gentle introduction to the theory of cluster algebras motivated by some geometric examples. I’ll try to describe a general framework for understanding cluster varieties. If time permits I’ll outline how Teichmüller spaces and spaces of laminations fit into this picture.

Speaker: Peter Crooks
Date: November 12, 2016
Title: Some compactifications in Lie theory‎
Abstract: I will discuss some techniques for compactifying varieties in Lie-theoretic contexts, with an emphasis on how such compactifications arise naturally from algebraic group actions.

Speaker: Payman Eskandari
Date: November 5, 2016
Title: Gross' proof of the Chowla-Selberg formula
Abstract: A classical formula of Chowla and Selberg expresses periods of an elliptic curve with complex multiplication up to an algebraic factor in terms of products of special values of the gamma function. Gross gave an algebro-geometric proof of this result in his 1978 Inventiones paper "On the Periods of Abelian Integrals and a Formula of Chowla and Selberg". I plan to sketch some ideas of Gross' proof.

Speaker: Bernd Schober
Date: October 22, 2016
Title: Resolution of singularities
Abstract:A starting point of algebraic geometry is the study of varieties, zero sets of polynomial equations. In general, a variety $ X $ may have singular points where information on the geometry of $ X $ is hidden. In order to understand this situation better one tries to find a model $ Y $ of $ X $ which shares many properties with $ X $, but which is easier to handle. One approach is to resolve the singularities. In 1964, Hironaka has proven the existence of such a model for varieties over fields of characteristic zero. The aim of this talk is to give a gentle introduction to resolution of singularities over the complex numbers. By discussing some examples, we will explore together the ideas and techniques developed from Hironaka's famous proof. If time permits, I will finally explain some obstruction which appear when we consider fields of positive characteristic.

Speaker: Fulgencio Lopez
Date: October 8, 2016
Title: Math of Musical Scale
Abstract:We will study the different frequencies of musical scales and how their history.

Speaker: Timothy Magee
Date: October 4, 2016
Title: Toric varieties, log Calabi-Yau's, and Combinatorial Representation Theory
Abstract: Roughly speaking, a log Calabi-Yau is a space that comes equipped with a volume form in a natural way. Let X be an affine log CY with volume form Ω. We can partially compactify X by adding divisors along which Ω has a pole. The set of these divisors says a lot about X's geometry-- for a torus (the simplest example of a log CY) this set is just the cocharacter lattice. We can actually give this set a geometrically motivated multiplication rule too, which I hope not to get into. But this multiplication rule allows us to construct an algebra A, defined purely in terms of the geometry of X, and conjecturally A is the algebra of regular functions on the mirror to X. Viewed as a vector space, A naturally comes with a basis-- the divisors we used to define it. So we get a canonical basis for the space of regular functions on X's mirror. All of the technology involved is a souped-up version of something from the world of toric varieties. I'll describe the picture for toric varieties first, then say how this fits into the broader log CY setting. Finally, many objects of interest to representation theorists (semi-simple groups, flag varieties, Grassmannians...) are nice partial compactifications of log CY's. This gives us a chance to use the machinery of log CY mirror symmetry to get results in rep theory. Maybe the most obvious application given what I've said so far is finding a canonical basis for irreducible representations of a group. I'll discuss this, as well as how this machinery reproduces cones that make combinatorial rep theorists feel warm and fuzzy inside (like the Gelfand-Tsetlin cone and the Knutson-Tao hive cone).

Speaker: Benjamin Briggs
Date: September 17, 2016
Title: Complex reflection groups, Duality groups, such and such
Abstract: I'll try to say something about the beautiful theory of complex reflection groups. We'll cover some classical things which, maybe, everyone should see. Then we'll talk about some of these reflection groups which satisfy a curious duality property, and what you can get out of it. Maybe we will talk about other things, like flag varieties. This is a matter of invariant theory, representation theory, and some nice geometry, but it should be very accessible to anyone who wants to come.

Speaker: Mykola Matviichuk
Date: August 21, 2016
Title: Deformation theory of Dirac structures via L infinity algebras
Abstract: A Dirac structure is a lagrangian subalgebroid in a Lie bialgebroid. One should think of Lie bialgebroids as a generalization of Lie bialgebras, which play a crucial role in the theory of Poisson-Lie groups. To any Dirac structure we associate a natural L infinity algebra (aka strong homotopy Lie algebra) governing deformation theory of the Dirac. The plan of the talk is to start with defining the relevant notions of Dirac geometry and motivate the problem. Then I will give the necessary background on L infinity algebras. Then I will try to explain our construction. Based on the audience demand, the plan can be modified as we go, or abandoned altogether. No background in Dirac geometry or L infinity algebras will be assumed.

Speaker: Elliot Cheung
Date: July 25, 2016
Title: Geometric Invariant Theory
Abstract: GIT is a way to study the equivariant geometry of varieties or schemes (especially in the projective case). A popular application of GIT is in the construction of coarse moduli spaces. In this context, GIT is a good tool for providing compactifications of such spaces. Unfortunately, it is often the case that the boundary of such a compactification has a "weaker modular meaning". One may partially resolve the singularities of a GIT quotient and provide an alternative compactification of these moduli spaces with better modular properties. In the GIT language: it's a resolution that turns all semi-stable points into either properly stable or unstable.

Speaker: Iordan Ganev
Date: April 11, 2016
Title: The wonderful compactification for quantum groups
Abstract: The wonderful compactification of a semisimple group links the geometry of the group to the geometry of its partial flag varieties, encodes the asymptotics of matrix coefficients for the group, and captures the rational degenerations of the group. It plays a crucial role in several areas of geometric representation theory, and can be realized as a quotient of the Vinberg semigroup. In this talk, we will review several constructions of the wonderful compactification and its relevant properties. We then introduce quantum group versions of the Vinberg semigroup, the wonderful compactification, and the latter's stratification by G x G orbits. The talk will include an overview of necessary background from the representation theory of reductive groups, and a discussion of noncommutative projective geometry.

Speaker: Peter Budrin
Date: April 2, 2016
Title: Laurence Sterne and Soviet Literary Scholars of the 1930s
Abstract: We will explore the reception of Laurence Sterne's novels in Stalin's Russia in the 1930s. In that tragic time of executions, arrests and the suppression of free thought an interesting and paradoxical discussion about the personality and works of the English comic author took place. The analysis is based both on published texts and archival materials: unpublished articles about Sterne, personal letters and documents of literary scholars of the 1930s.

Speaker: Krishan Rajaratnam
Date: March 26, 2016
Title: Laurence Sterne and Soviet Literary Scholars of the 1930s
Abstract: We will explore the reception of Laurence Sterne's novels in Stalin's Russia in the 1930s. In that tragic time of executions, arrests and the suppression of free thought an interesting and paradoxical discussion about the personality and works of the English comic author took place. The analysis is based both on published texts and archival materials: unpublished articles about Sterne, personal letters and documents of literary scholars of the 1930s.

Speaker: Anne Dranovski
Date: March 19, 2016
Title: Some Motivation for Geometric Representation Theory
Abstract: We'll reveal the why and how of the flag variety: where it comes from, and how it's used. On the how end, we'll recite a handful of fancy dualities, including, you guessed it, Howe duality. Examples may be ramped up from sl_2 to sl_3, though always over C.

Speaker: Justin Martel
Date: March 5, 2016
Title: Virtual Cohomological Dimension and Borel-Serre Formula
Abstract: I look to describe some homological-duality problems related to the arithmetic groups SL(2,Z), Sp(4,Z), connectivity of their rational Tits buildings and Borel-Serre rational bordifications of the correspondant symmetric spaces.

Speaker: Anton Izosimov
Date: February 27, 2016
Title: Integrable systems and Riemann surfaces
Abstract: I will give an informal review of the theory of integrable systems from the point of view of algebraic geometry. In particular, I will prove a classical result saying that integrable systems could be linearized on the Jacobian of the spectral curve. The talk will be based on simple (nevertheless,quite general) examples.

Speaker: Özgür Esentepe
Date: January 30, 2016
Title: Some Motivation for Noncommutative Algebraic Geometry
Abstract: In the classical theory of algebraic geometry, there is a very nice correspondence between certain points on certain topological spaces and certain ideals of certain rings. Similarly, in representation theory, there is a very nice correspondence between certain ideals of certain rings and certain modules over those rings. Then, certain French mathematicians in certain decades of last century said that we should change our understanding of spaces and they introduced sheaves, and they established yet another correspondence between certain sheaves and certain of modules. This all happened in the commutative case. I will talk about what happens in noncommutative algebra and how certain modules act like points of certain so called noncommutative spaces.

Speaker: Changho Han
Date: January 16, 2016
Title: Why moduli spaces
Abstract: Moduli spaces is a roughly 100 years old concept that changed the way mathematicians think. We will explore various significance of moduli spaces as families and will focus on examples. Examples will mainly be from algebraic geometry.

Speaker: Eduard Duryev
Date: November 25, 2015
Title: Knots, Links and 3-manifolds
Abstract: This semester I was trying to get closer to such objects as knots, links and 3-manifolds. Various people were telling me interesting stories and I want to share some of them with you. My talk will be rather an amateur bus trip (if you know what I mean) by the colorful sights of topological wonders rather than a deep investigation of the topic. In particular, we will perform a dance with Seifert surfaces and make a surgery of the trefoil knot complement in the 3-sphere to extract its Alexander polynomial - a powerful invariant of knots and links. We will see how Thurston norm on the homologies of 3-manifolds, a younger sibling of Alexander polynomial, keeps record of all fibrations of this manifold over the circle.
And here are some questions you might want to bring to our trip:
Is there a foliation of a 3-sphere by smooth surfaces?
Why figure-8 knot complement is a hyperbolic 3-manifold?
Can you visualize a circle bundle over a torus with Chern class equal to 1?

Speaker: Petr Pushkar
Date: November 14, 2015
Title: Borel-Weil-Bott Theorem and Weyl Character Formula
Abstract: I will present the one of the most basic interactions of Representation Theory and Geometry. There are many different ways to prove the Weyl character formula using just representation theory, I will show how to deduce it from the geometrical properties of the flag variety.

Speaker: Dylan William Butson Esquire
Date: November 7, 2015
Title: Rational Homotopy Theory
Abstract: Some elements of Sullivan's approach to rational homotopy theory: homotopy theory in the categories of spaces, simplicial sets and differential graded algebras, the relationship between them, and in particular a practical method to compute the rational homotopy groups of spaces from their dgas of differential forms.

Speaker: Louis-Philippe Thibault
Date: October 31, 2015
Title: McKay Correspondence
Abstract: The McKay correspondence describes a relationship between resolution of Kleinian singularities and representation theory of finite subgroups of SU(2, C). It gave rise to many interesting questions and results linking resolution of singularity, Auslander-Reiten theory and representation theory of algebras, as well as string theory, amoung others. In this talk, we will describe the correspondence and show some of its nice consequences. We will try to give an historical account, starting with some work of Plato and DaVinci.

Speaker: Ivan Telpukhovskiy
Date: October 24, 2015
Title: On Moduli Space of Algebraic Curves
Abstract: I will give a talk on moduli space of algebraic curves. This is an important subject of study in algebraic geometry. I will start with examples in small dimensions, describe Deligne-Mumford compactification and maybe reach ELSV formula.

Speaker: Leonid Monin
Date: xx
Title: Tait-Kneser Theorem
Abstract: xx

Speaker: Gaurav Patil
Date: October 3, 2015
Title: Taniyama-Shimura Conjecture
Abstract: xx

Speaker: Parker Glynn-Adey
Date: September 12, 2015
Title: q-Homotopy for Simplicial Complexes
Abstract: In the 1970s R.H. Atkin developed tools for studying connectivity properties of simplicial complexes in a series of strange papers. The resulting theory of q-connectedness was applied in many novel contexts but has since fallen in to disuse. The theory has been entirely neglected by topologists (perhaps because it was invented by a physicist and it is not a homeomorphism invariant). This talk will introduce the modern treatment of q-connectedness as a homotopy theory for combinatorial simplicial complexes. We'll apply it by computing some weird groups related to the Platonic solids and, time permitting, some buildings.

Speaker: Vincent Gelinas
Date: July 12, 2015
Title: Cyclic Homology
Abstract: xx

Speaker: Benjamin Briggs
Date: xx
Title: An Introduction to Derived Categories
Abstract: xx

Speaker: Leonid Monin
Date: xx
Title: Tropics and Gromov-Witten Invariants
Abstract: xx

Speaker: Leonid Monin
Date: xx
Title: Flat Surfaces
Abstract: xx

Speaker: Leonid Monin
Date: xx
Title: On Bernstein-Kouchnirenko Theorem
Abstract: xx