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The Graduate Student Colloquium is a series of talks, generally organized monthly, that allow graduate students to present their work in a fun, non-stressful setting. It's a great way to both practice your presentation skills and to share your work with your peers! If you are interested in giving a talk for the colloquium, please send us an email at ottawamathconference@gmail.com.
Upcoming Colloquium
Date and time: Wednesday, October 1, 2025 from 2-3pm
Room: STEM 364
Speaker: Ömer Avci
Affiliation: University of Ottawa
Title: Torsion of Rational Elliptic Curves over the Galois Extensions of $\mathbb{Q}$
Abstract: Mazur's celebrated theorem gives a complete classification of the torsion subgroups $E(\mathbb{Q})_{\mathrm{tors}}$ for elliptic curves $E/\mathbb{Q}$. This result inspired the broader problem of classifying $E(L)_{\mathrm{tors}}$ for elliptic curves $E/L$, where $L$ is a field of characteristic zero. In this talk, I will first review results from the literature and some variants of this problem. I will then focus on the case where $L/\mathbb{Q}$ is a Galois extension, outlining our methods and presenting two families of results: when $L = \mathbb{Q}(\zeta_p)$ for a prime $p$, and when $L$ is a $\mathbb{Z}_p$-extension of a quadratic field $K$.
Past Colloquia
Date and time: Monday, June 16, 2025 from 2-3pm
Room: STEM 464
Speaker: Geoff Vooys
Affiliation: University of Calgary
Title: Getting Ecstatic over the p-adic
Abstract: Have you ever thought that your number system is too Archimedian? Have you ever wanted to have a complete space whose closed unit ball is a disk? Have you ever wanted a complete topological field whose elements have descriptions which indicate infinitesimal information in clear and precise ways? Well, you happen to have very specific desires, but I have the thing for you: p-adic numbers! More natural than the real numbers (in the sense that Ostrowski's Theorem says with probability 1 if you pick a random completion of the rational numbers you pick a p-adic field), the p-adic numbers are fields which are of great interest in modern algebraic geometry, algebraic number theory, Langlands Programme related areas, and other places where ultrametric spaces rear their heads. In this talk I'll give a gentle introduction to the p-adic numbers, give many perspectives on how they arise and can be written (clickbait: this connection with the Cantor set WILL shock you!), and other fun facts about what they can do for you. The only pre-requisites for this talk are a general knowledge of what a metric space and its completion are, what a prime number is, and a sense of wonder.
Speaker bio: Geoff Vooys is a postdoctoral scholar at the University of Calgary working with Robin Cockett and Kristine Bauer. Prior to this, Geoff was a sessional instructor at Mount Allison University, an AARMS postdoctoral scholar at Dalhousie University working with Dorette Pronk, a sessional instructor at the University of Lethbridge, and a graduate student at the University of Calgary (his thesis was in the Local Langlands Programme under the supervision of Clifton Cunningham and involved studying the equivariant derived category). Geoff's research primarily focuses on categorical geometry in tangent-categorical, algebraic-geometric, and sheaf-theoretic flavours. Geoff also likes to write expository things which ''simplify'' things by explaining how they're secretly category theory in disguise and likes to find ways to argue that any p-adic topology is strictly better than any Archimedian topology.
Additionally, Geoff is technically and legally also a human being and enjoys hobbies which embrace these facts. For instance: Geoff enjoys playing and coaching rugby, playing terrible video games, reading, spending time with his family (especially his partner and his two pugs), and existing.
Date and time: Thursday, April 3, 2025 from 1-2pm
Room: STEM 664
Speaker: Elise Woodward
Affiliation: University of Ottawa
Title: Does the Early Bird Always Get the Worm? Evolution of Emergence Times in Consumer-Resource Systems
Abstract: Spring is coming, so when should a species emerge from its winter rest? What happens in the long term when consumer and resource emergence times are mismatched? In this talk I explain and derive a semi-discrete consumer-resource system to explore the question of mismatched emergence. I’ll explain how we investigated the evolutionary dynamics that arise when emergence times are considered a heritable trait with mutations. We’ll go through simulations of the model to explore how the mean and variance of the emergence time distribution, as well as the total population density, evolve. Depending on initial conditions, we’ll find different outcomes such as an evolutionary arms race to increasingly early emergence times, or convergence to steady states. This work is based on the research of Dr. Frithjof Lutscher, Sarah Abel and myself. Hope to see you there!
Date and time: Friday, January 31, 2025, from 2:30-3:30pm
Room: STEM 464
Speaker: Khalil Besrour
Affiliation: University of Ottawa
Title: Vector-Valued Modular forms and How to construct them
Abstract: In this talk, we begin by introducing the classical notion of modular forms, which are fundamental objects in number theory and play a key role in various areas of number theory and mathematical physics. We then discuss one of their generalizations, known as vector-valued modular forms. These objects arise in contexts where modular forms transform according to higher-dimensional representations of the modular group. Finally, we present some of the key techniques and methods used to construct vector-valued modular forms, highlighting their importance and applications in both theoretical and applied mathematics.
Date and time: Wednesday, December 11, 2024 from 3-4pm
Room: STEM 664
Speaker: Zachary Brannan
Affiliation: University of Ottawa
Title: Utilising Treewidth to Approximate High Dimensional Optimal Transport problems for Quantum Chemistry
Abstract: In Electronic Structure theory it is know that the ground state energy of a system is determined by the electronic density instead of the wave function. This seemingly reduces the dimensionality of the problem, as for an N-electron system the wave function has 3N arguments and the electron density only has the 3 spacial coordinates as arguments.
Unfortunately, the functional one needs to minimise to solve for the electron density involves an optimal transport problem that is itself a 3N dimensional problem. Current techniques involve considering the non-interacting limit where the contribution of this optimal transport problem is negligible.
This talk will focus instead on ways that we can approximate this optimal transport problems with lower dimensional objects. This will be done be representing the high dimensional problem as the summation of problems of varying dimensions. Identifying each of these problems with graphs allows us to quickly use a graph property call treewidth to identify which of these problems are easily calculated for the approximation.
Date and time: Wednesday, November 13th from 2:30 to 4:00 pm
Location: STEM 664
Speaker: Juan Jiménez
Title: The past light-cone property of the stochastic wave equation with heavy-tailed noises
Abstract: The study of stochastic partial differential equations (SPDEs) with heavy-tailed noises is partly driven by the need to explain the stochastic behavior of systems with abrupt changes. Heavy-tailed noises are useful in modeling a wide variety of discontinuous phenomena such as financial crashes, turbulent flows, and certain types of cosmic radiation. Classical models like Brownian motion were initially used to describe continuous random fluctuations, but they proved inadequate for systems exhibiting large, random jumps.
In this talk, we will show the existence and uniqueness of a solution to the stochastic wave equation in $\mathbb{R}^d$ with $d \leq 2$, driven by a Lévy noise which may have infinite moments of any order. By leveraging the past light-cone property of the wave operator, we will prove the existence of a unique random field solution under the integrability assumption $\int_{|z| \leq 1} |z|^p \nu(dz) < +\infty$ for some $p \in (0,2)$, where $\nu$ is the Lévy measure associated with the noise. Moreover, this solution has bounded $p$-moments up to a certain stopping time relative to the light-cone region. Based on https://doi.org/10.1016/j.spa.2024.104479.
Bio: Juan Jiménez is a fourth-year PhD student at the University of Ottawa, supervised by Professor Raluca Balan. His doctoral research focuses on stochastic partial differential equations driven by heavy-tailed noise, particularly on the existence and uniqueness of solutions and their qualitative behavior.
Date and time: Tuesday, October 29th from 3:00 to 4:00 pm
Location: STEM 664
Speaker: Rieli T. Gomes dos Santos
Title: The Physics of Spontaneous Symmetry Breaking: the Goldstone's Theorem and Beyond
Abstract: This talk will explore the fundamental concepts of spontaneous symmetry breaking (SSB), focusing on the theoretical framework and its implications in various physical systems. We will begin with an introduction to the basic notions of SSB, followed by presenting Goldstone's theorem and classifying the resulting Nambu-Goldstone (NG) modes, distinguishing between Type-A and Type-B modes. The discussion will delve into the low-energy effective Lagrangian theory, highlighting key properties of SSB. Throughout the presentation, a range of examples will be used to show the consequences of SSB in physical systems and enhance our understanding of the underlying physics.
Bio: Rieli is a second-year Master's student in Physics at the Londrina State University/Brazil, under the supervision of Prof. Pedro Sergi Gomes and Prof. Paula Bienzobas. Her research focuses on Quantum Field Theory, emphasizing spontaneous symmetry breaking and higher-form symmetries. Rieli has been awarded a Mitacs/Fundação Araucária scholarship to conduct a research project at the University of Ottawa on Quantum Optimal Transport as a Visiting Research Student, under the supervision of Prof. Augusto Gerolin in the Department of Mathematics and Statistics from July to November 2024.
Date and time: Thursday, September 26th from 3:00 to 4:00 pm
Location: STEM 464
Speaker: Mico Luo
Title: Modification-Tolerant Digital Signatures using Combinatorial Group Testing
Abstract: Matrices that are d-cover-free are used in non-adaptive combinatorial group testing (CGT). They allow for locating up to d defectives within a set of n items by testing them in groups. In this talk, we study d-cover-free families (CFFs) built from set systems and codes, with a focus on CGT decoding algorithms to identify defectives from test results. This talk also explores the application of non-adaptive combinatorial group testing using d-CFF to digital signatures. This method not only verifies the authenticity of the signature but also locates up to d allowed modifications, leading to what is known as d-modification tolerant signature schemes.
Bio: Mico has recently submitted her master's thesis under the supervision of Lucia Moura. Her research focuses on combinatorial designs and cryptography. In her free time, she enjoys playing video games and reading novels.
Date and time: Thursday, August 29th from 3:00 to 4:00 pm
Location: STEM 664
Speaker: Amélie Comptois
Title: The Rich World of Enriched Categories
Abstract: A category is made up of a collection of objects and a collection of maps between them called morphisms. For any choice of objects X and Y, we call the set of morphisms from X to Y a Hom-set, often denoted Hom(X,Y). Interestingly, it is often the case that Hom(X,Y) is more than just a set. A category can have Hom-vector-spaces, Hom-topological-spaces, or some other “Hom-things”. We say a category C is enriched over another category V if the “Hom-things” of C are objects of V. It turns out that some well-known algebraic structures arise as examples of enriched categories. This talk aims to motivate through examples and then clearly define enriched categories and enriched functors. No prior knowledge of category theory is required.
Bio: Amélie is a second-year master’s student in mathematics, working in category theory under the supervision of Rick Blute and Rory Lucyshyn-Wright. Her research focuses on categories graded by monoidal categories. These structures simultaneously generalize enriched categories and categories.
Date and time: Wednesday, July 31st from 3:00 to 4:00 pm
Location: STEM 664
Speaker: Archishman Sasha
Title: Second Order Differential Geometry and Stochastic Calculus in Manifolds
Abstract: In differential geometry, we often think of tangent vectors as first-order differential operators in manifolds. In second order differential geometry, we concern ourselves with second order differential operators. It provides a convenient toolkit for studying stochastic calculus in manifolds. Not only does it help to generalize stochastic calculus in Euclidean spaces, but it also allows us to convert problems in stochastic calculus to problems in geometry, as well as giving probabilistic interpretations of certain differential geometric objects. In this talk, we will explore some of these connections. We will introduce manifold versions of two well-known notions in stochastic calculus, the Itô and Stratonovich integrals, as special cases of a general second order stochastic integral on manifolds. Following this, we will discuss stochastic differential equations (SDEs) on manifolds, and time permitting, we will look into reduction and reconstruction of symmetric SDEs on manifolds.
Bio: Archishman is a third-year Ph.D. student in math under the supervision of Prof. Tanya Schmah and Prof. Cristina Stoica. His research involves studying stochastic generalizations of Lagrangian and Hamiltonian mechanics on manifolds. He also enjoys dabbling in music, biking, travelling, and exploring different cuisines.
Date and time: Friday, June 28th from 3:00 to 4:00 pm
Location: STEM 664
Speaker: Prangya Parida
Title: Generalizations of cover-free families based on hypergraphs
Abstract: In this talk, we explore the concept of cover-free families (CFFs) and introduce their generalization using hypergraphs. Traditional CFFs are families of subsets of a finite set where no subset is contained in the union of a fixed number of other subsets. Cover-free families have applications in group testing, information retrieval, cryptography, and more. We extend this concept by defining cover-free families on hypergraphs, where edges of the hypergraph specify the sets of columns whose union must not cover any other column. This generalization encompasses traditional CFFs as a special case and provides a richer combinatorial framework. We will discuss foundational results, new constructions, and ongoing research on hypergraph-based CFFs, highlighting their potential to optimize group testing.
Bio: Prangya is a fourth-year Ph.D. student in mathematics, working in the area of combinatorial arrays under the supervision of Prof. Lucia Moura. Her research focuses on the generalization of cover-free families based on hypergraphs.
Date and time: Tuesday, April 30th from 3:30 to 4:30 pm
Location: STEM 664
Speaker: Khalil Besrour
Title: A Tale of Modular Foms and L-functions
Abstract: Modular forms are fundamental mathematical entities with applications spanning various domains, including number theory, representation theory, and mathematical physics. Their significance is notably highlighted in the proof of Fermat’s Last Theorem, attributed to the Shimura-Taniyama-Weil conjecture asserting the modularity of elliptic curves. A vital link between modular forms and arithmetic is established through L-functions, exemplified by the Riemann ζ-function. In this Colloquium, we will be introducing the attendees to the world of modular forms and their applications.
Bio: Khalil Besrour is a 3rd year PhD student working under the supervision of Abdellah Sebbar. His research area covers modular forms (classical, vector valued and p-adic), elliptic curves and equivariant functions.
Date and time: Thursday, March 21st from 4:30 to 5:30 pm
Location: STEM 664
Speaker: Autumne Cadieux
Title: Got (too much) milk? Investigations into the treatments and indications of iron deficiency anemia in children.
Abstract: Have you ever considered if you drink way too much milk? Well for the average adult, this doesn’t usually cause too many problems, but for a young child, this can lead to a lack of iron storage within their bodies, and this can lead to iron deficiency anemia (IDA). But what do we do when a child presents with IDA? What are the common treatments, and which is most effective for each individualized case? The goal of this research work was to investigate the key indicators and treatments of IDA to support evidence-based decision making for clinicians treating IDA in the pediatric emergency department.
Bio: I am a second year MSc Statistics student, aiming to submit my thesis in the coming weeks. My work centers around applied biostatistics, particularly within the field of pediatric healthcare. I am interested in many facets of applied statistics, specifically with applications to Indigenous well-being, economic prosperity and healthcare, a field in which I would like to explore in future work.
Date and time: Tuesday, February 13th from 4:00 to 5:00 pm.
Location: STEM 664
Speaker: Daniel Dallaire
Title: A category linking planar graph colouring to sl_2-representation theory
Abstract: The chromatic category is a diagrammatic monoidal category which encodes information about the proper colourings of planar graphs. Although it is related to graph colouring from its usual definition, it can also be constructed in a representation theoretic context as well. This yields an interesting connection between the problem of colouring planar graphs (in particular, the four colour theorem) and the representation theory of the lie algebra sl_2. In this talk, I will introduce the chromatic category and discuss how it can instead be constructed as a category of representations.
Bio: I am a 2nd year M.Sc. student in the department of Mathematics and Statistics here at the University of Ottawa with a background in math, stats, and computer science. My current research interests involve string diagrams, categorification, and representation theory, however I am interested in a variety of math and stats topics.
Date and time: Tuesday, January 30th from 4:30 to 5:30 pm.
Location: STEM 664
Speaker: John Tsang
Title: On the use of machine learning procedures for the treatment of unit nonresponse in surveys
Abstract: There has been a significant interest in machine learning in national statistical offices in recent years. Thanks to their flexibility, these methods may prove helpful at the nonresponse treatment stage. We conduct an empirical investigation to compare several machine learning procedures in terms of bias and efficiency. In addition to the classical machine learning procedure, we assess the performance of ensemble approaches that use different machine learning procedures to produce a set of weights adjusted for nonresponse.
Bio: John is a graduate student in the Department of Mathematics and Statistics at the University of Ottawa. His primary research interests include the theory and application of survey sampling with missing data and statistical learning. With a background in economics and computer science, he is also interested in forecasting, econometrics and parallel computing.
Date and time: Thursday, December 7th from 5:00 to 6:00 pm.
Location: STEM 464
Speaker: Joe Ghafari
Title: Introduction to stochastic partial differential equations
Abstract: Stochastic partial differential equations (SPDE) are PDE with ”noise”. A very large class of singular SPDE remained open problems and unsolved for decades, until 2011, when Martin Hairer solved the KPZ equation using rough paths theory and later, in 2013, he introduced a new theory of ”regularity structures” allowing to give a rigorous meaning and solve many SPDE arising from physics and consequently earning a medal fields for his work. In this talk, we give a gentle introduction on SPDE. After defining them, we will outline examples and challenges of singular SPDEs and along the way we discuss formally the sub-criticality of these equations. Lastly, we present briefly three techniques allowing to solve SPDE: Martin Hairer theory of regularity structures, Paracontrolled distributions (Gubinelli, Imkeller and Perkowski), and renormalization group (Kupiainen). An effort has been made to keep the exposition concise and self-contained.
Bio: I am a second PhD student at the university of Ottawa, co-supervised by Jeremy Quastel (university of Toronto) and Aaron Smith (university of Ottawa). My research interests are: stochastic calculus and stochastic partial differential equations.
Date and time: Thursday, November 16th, from 4:00 - 5:00 PM
Location: STEM 464
Speaker: Omar Cayley
Title: How L_\infty is isomorphic to ℓ_\infty
Abstract: In functional analysis, we know that the space $L_p$ is not isomorphic to $ℓ_p$ for every $p\geq 1$ except for $p = 2$. It is somewhat a surprising fact that the Banach spaces $L_\infty$ and $ℓ_\infty$ are isomorphic. In this talk, we will prove this using a method that was first introduced by the Polish mathematician Aleksander Pełczyński in 1958. This result illustrates another consequence of the axiom of choice.
Bio: I am a first year PhD student. My research focuses on nonlocal games, or quantum information theory generally. I am glad to be serving as a committee member of the MSGSA for the first time. In my free time I like to watch the news or play chess, I also enjoy hiking and exploring new grounds.
Date and time: Friday, September 15th, from 4:00 - 5:00 PM
Location: STEM 464
Speaker: Maruša Lekše
Title: The spouse-loving variant of the Oberwolfach problem
Abstract: At the conference in Oberwolfach there was a tradition for participants to have dinner together each evening of the conference. In 1967 Gerhard Ringel asked the following question: given a room with t round tables of sizes ℓ1, . . . , ℓt , is it possible for people to sit around those tables in such a way that over an appropriate amount of meals, every person sits next to every other person exactly once? Or equivalently, given integers ℓ1, . . . , ℓt ≥ 3 , with n = ℓ1 +. . .+ ℓt being an odd integer, does there exist a decomposition of the complete graph Kn into copies of a graph F, where F is a disjoint union of t cycles of lengths ℓ1, . . . , ℓt?
A lot of results have been obtained on this problem and its many variants, but in general it still remains unsolved. In this talk, we will focus on one of the recently studied variants - the spouse loving variant, in which the participants at the conference are couples, and every person wants to sit next to every other person exactly once, except for their spouse, next to whom they want to sit exactly twice. OP +(ℓ1, . . . , ℓt) has been previously solved for the case when all ℓi are even, the case when ℓ1 = . . . = ℓt , as well as the two-table case when one table has size 3, and we will look at some of these constructions. We will then present a new result on the two-table spouse-loving variant.
Bio: Maruša Lekše is a second year Ph.D. student at the University of Ljubljana, Slovenija. This summer she worked on the Oberwolfach problem under the supervision of Prof. Mateja Sajna. Besides mathematics, she enjoys hiking, diving and playing board games.
Date and time: Wednesday, July 26th, from 4:00 - 5:00 PM
Location: STEM 664
Speaker: Antoine Velut
Title: Introduction to p-adic numbers and local fields
Abstract: The p-adic numbers have come to play a central role in modern number theory, with applications in class field theory, Iwasawa theory, Hodge theory and many others. Moreover, they are accessible right from the undergraduate level. Yet they are not a part of the usual mathematics courses, so they might still be unfamiliar to many.
In this talk, I will give an elementary exposition of their construction, while focusing on giving visual intuition of what this non-archimedean world looks like. I will then present some properties of the more general local fields, which encompass the p-adics, and explain some of the links with algebraic number fields.
Bio: Antoine Velut is a graduate student at the ENS de Lyon in France. He is at uOttawa for a summer internship under the supervision of Antonio Lei.
Date and time: Wednesday, June 28th, 2023, from 4:00 - 5:00 PM
Location: STEM 664
Speaker: Mihir Deo
Title: Factorization of unbounded p-adic L-functions
Abstract: p-adic L-functions are the power series with coefficients in the p-adic rings like Z_p and they p-adically interpolate special values of classical L-series attached to arithmetic objects such as modular forms. For example, let f = Σ a_n q^n be a modular form of weight k ≥ 2 which is p-ordinary, i.e. p does not divide its p-th Fourier coefficient a_p. Then, the p-adic L-function L_(p,f) attached to f is an element of the Iwasawa algebra Q_p ⊗ Z_p[[T]]. One could ask what happens if p | a_p. Then we get two p-adic L-functions L(p,f,α_i), i ∈ {1, 2}, where α_i are roots of X^2 − a_p X + p^(k−1). In this case, both power series have unbounded denominators and are no longer elements of Iwasawa algebra. In general, let F_α, F_β be two power series over a finite extension of the field of p-adic numbers Q_p satisfying certain interpolation formulae. Suppose further that the coefficients of the power series have unbounded denominators satisfying certain growth condition. In this talk, we will discuss the decomposition of F_α and F_β into linear combinations of two power series with integral coefficients. This is a part of my ongoing project which deals with the factorization of two variable p-adic L-function attached to a Bianchi modular form.
Bio: Mihir Deo is a PhD student under the supervision of Prof. Antonio Lei. Mihir did his undergraduation in Electronics engineering from University of Mumbai and then M.Sc. in Mathematics from IIT Gandhinagar. His research interests are p-adic L-functions and Iwasawa theory, arithmetic aspects of automorphic forms and p-adic Hodge theory.
Date and time: Thursday, March 23rd, from 4:30 - 5:30 PM
Location: STEM 664
Speaker: Masoomeh Akbari
Title: On the generalized Honeymoon-Oberwolfach Problem
Abstract: One of the most interesting problems in graph theory is the Oberwolfach Problem (OP), which was first presented by Gerhard Ringel in 1967. The OP asks whether it is possible to seat the n participants at a conference at t round tables of sizes m_1, m_2, … , m_t, where m_1+m_2+....+m_t = n, for several consecutive nights so that each person sits beside every other person precisely once.
In my thesis, I focus on a variant of the Oberwolfach Problem called the Honeymoon Oberwolfach Problem (HOP), which was introduced by Sajna. In this variation, we have 2n participants consisting of n newlywed couples. We want to see whether it is possible to seat them at t round tables of specified sizes for several consecutive nights so that each participant sits next to their spouse every time and next to each other participant exactly once. Some cases of HOP have been solved, and results have been published recently. However, some interesting and important cases are left unsolved. Moreover, HOP has been defined with the constraint that each table size is at least 4. In this research, I aim to generalize the problem to allow for tables of size two.
Bio: Masoomeh Akbari is a third-year Ph.D. student in mathematics. She works in the area of Graph Theory under the supervision of Prof. Sajna. She is doing research on the honeymoon Oberwolfach problem as her Ph.D. thesis. Besides academia, she enjoys traveling, walking, a warm cup of tea, and socializing with friends.
Date and time: Thursday, February 16th, 4:30PM - 5:30PM
Location: STEM 464
Speaker: Xiao Liang
Title: Distributionally robust optimization with covariate information in a non-parametric framework
Abstract: In this project, we consider distributionally robust optimization programs where the distribution of the uncertain parameters is only observable through a training dataset. We seek decisions that perform best in terms of the worst-case distribution within Wasserstein ambiguity ball, which is constructed in a non-parametric way. These theoretical results will be exemplified in the mean-risk portfolio selection problem, a major issue in financial engineering. No prior knowledge of optimization is necessary, and the emphasis of this presentation is on motivation and intuition rather than technical completeness.
Bio: Xiao Liang is a third year PhD student under the supervision of Professor Raluca Balan. His main research focus is on stochastic partial differential equations. He is also interested in robust optimization and applied econometrics dealing with panel data.
Date and time: January 26th 2023, 4:30pm - 5:30pm
Location: STEM 464
Speaker: Samuel Desrochers
Title: If you’ve heard of Universal Properties, then you can understand Adjoint Functors
Abstract: Have you ever come across the notion of a “universal property”, and wondered what that really means? Or have you heard a category theorist talk about “adjoint functors”, but failed to understand what they are or why they’re interesting? In this presentation, I’ll address both of these questions! Using examples of universal properties as motivation, I’ll explain what adjoint functors are, how they come about, and why people study them. No prior knowledge of category theory is necessary, but knowing some examples of universal properties might help you relate more to the presentation.
Date and time: December 1st 2022
Location: STEM 664
Speaker: Lord Kavi
Title: Hamming Graphs and 3-independent sets.
Abstract: An independent set, also known as a stable set or coclique, in a graph is a set of vertices, no two of which are adjacent. The size of a largest independent set is called the independence number. A k-independent set in a graph is a set of vertices such that any two vertices in the set are at distance at least k+1 in the graph. The k-independence number of a graph is the size of a largest k-independent set in the graph.
Using interlacing, Abiad et al generalized the Hoffman spectral bounds on k-independence, which involves taking polynomials of degree at most k. By getting the right choice of a polynomial we present a spectral bound on the 3-independence number of graphs and apply this bound to well-known families of graphs. We investigate tightness of this bound on the Hamming graph H(d; q). In particular, we give a construction of 3-independent sets in H(d,2) and show tightness of the bound for d = 2^r and d = 2^(r-1) with r in Z+.
Date and time: November 9th 2022
Location: STEM 464
Speaker: Cesar Bardomiano
Title: A first look into infinity categories
Abstract: Since their discovery, categories have proven to be a natural and powerful tool to do mathematics. They are particularly useful for establishing relations between different mathematical objects. Moreover, category theory is ubiquitous to mathematics even though this may not be apparent to the working mathematician. On the same stream of ideas, categories, as mathematical objects, should be able to study themselves. This leads us to higher categories.
The goal of this talk is to introduce to the general audience the idea of an infinity-category. We will motivate this notion from two points of view, one coming naturally from categories and the other from algebraic topology. To this end, we will review examples from basic categorical concepts and generalize these ideas to the higher setting. From topology, we will see a particular infinity-category which is the infinity-groupoid of a space.
Bio: Cesar Bardomiano Martinez is a PhD student at the department under the supervision of Simon Henry, working primarily in foundational aspects of higher category theory and its relations with logic.
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