Transformation Groups Seminar

Speaker: Larry So (Western)

"The quotient construction and homogeneous coordinates of toric varieties"

Time: 10:30

Room: MC 108

Algebraic Geometry

Speaker: Kate Kim (Western)

"WAG: 0-dimensional ideals"

Time: 15:30

Room: MC 108

Graduate Seminar

Speaker: Marwa Tuffaha (Western)

"Mutator dynamics cannot be explained by mutation rates alone"

Time: 16:30

Room: MC 107

Mutators, cells with elevated mutation rates, are common in both natural microbial populations and in human cancers. Recent experiments have shown that mutators can invade a population, but the invasion dynamics and probability couldn’t be explained by mutation rates alone. Here we show, analytically and in simulation, that mutation bias (which types of mutations are likely to occur) can play an important role in the emergence of mutators. A mutator that reduces or reverses the historically prevailing mutational bias is shown to have an increased chance of invasion, while chances are reduced when the bias is reinforced. These findings are important when trying to understand natural populations or competition experiments with mutators.

Transformation Groups Seminar

Speaker: (Western)

"Polytopes and Toric Varieties"

Time: 10:30

Room: MC 204

Algebraic Geometry

Speaker: Michael Francis (Western)

"WAG: Primary Decomposition"

Time: 15:30

Room: MC 107

Department Meeting

Speaker:

"Department Meeting"

Time: 15:30

Room: TBA

Transformation Groups Seminar

Speaker: Sayantan Roy Chowdhury (Western)

"Toric regularity (cancelled)"

Time: 10:30

Room: MC 204

Algebraic Geometry

Speaker: Greg Reid (Western)

"WAG: Linear PDE's with constant coefficients"

Time: 15:30

Room: MC 107

Colloquium

Speaker: George Shillcock (University of Oxford)

"Evolution Theory Talk - Division of labour"

Time: 15:40

Room: MC 204

A collective evolves division of labour when its members all benefit by specialising to perform complementary tasks. It is observed across various scales of biological organisation at the origins of multicellularity and eusociality. It is, therefore, of interest to understand the conditions which favour the evolution of division of labour by natural selection. By focusing our attention to collectives that reproduce clonally, such as many plants and bacteria, we may safely model collectives as fitness maximisers faced with a constrained optimisation.

Geometry and Topology

Speaker: Steven Amelotte (Western)

"Homotopy types of moment-angle complexes and minimal free resolutions of Stanley-Reisner rings"

Time: 15:30

Room: MC 107

Toric topology assigns to each finite simplicial complex K a space with a torus action, called the moment-angle complex, whose equivariant topology neatly reflects combinatorial properties of K and homological properties of the Stanley-Reisner ring of K. A central result in the subject identifies the cohomology of the moment-angle complex with the Koszul homology of the corresponding Stanley-Reisner ring. In this talk, I'll describe how cohomology operations induced by the torus action can be used to extend this result to a topological interpretation of the entire minimal free resolution of the Stanley-Reisner ring, and then outline some work in progress which aims to identify the homotopy types of certain moment-angle complexes in terms of this data. (This is all based on joint work with Ben Briggs.)

Pizza Seminar

Speaker: Lindi Wahl (Western)

"Generating predictions: the power and elegance of generating functions."

Time: 17:00

Room: MC 107

Like other transform methods, generating functions sometimes offer a lens through which an otherwise complicated problem has a surprisingly elegant solution. I'll offer a quick introduction to probability generating functions and show how we can take advantage of some really beautiful theorems to make practical predictions -- like the probability that COVID-19 has driven the Yamagata flu strain to extinction.

Ph.D. Presentation

Speaker: Third-year Ph.D. students (Western)

"TBA"

Time: 15:30

Room: MC 107

Graduate Seminar

Speaker: Thomas Thorbjornsen (Western)

"The Synthetic Fundamental Group of the Circle"

Time: 16:30

Room: MC 107

Homotopy type theory is a foundation for mathematics that is well-suited to do homotopy theory. Unlike ZFC, we no longer have access to the law of excluded middle or the axiom of choice. Many mathematicians find it daunting and off-putting to work without these axioms, but great opportunity is created amidst the challenge.

In this talk we will investigate how we can do homotopy theory in homotopy type theory. We will construct the fundamental group of the circle by using the tools provided by Martin-Löf type theory, Voevodsky’s univalence axiom, and higher inductive types. In particular, we will look at the underlying language of type theory and its identity types, how fiber bundles are expressed as type families, and the essential role played by the univalence axiom.

Transformation Groups Seminar

Speaker: Sayantan Roy Chowdhury (Western)

"Toric regularity"

Time: 10:30

Room: MC 204

Algebraic Geometry

Speaker: Meagan James (Western)

"WAG: Elimination"

Time: 15:30

Room: MC 107

Geometry and Topology

Speaker: Rasul Shafikov (Western)

"Special embeddings in complex analysis"

Time: 15:30

Room: MC 107

Since Whitney's classical result of smooth embedding of manifolds into $\mathbb R^n$, one of the themes in geometry has been the existence of embeddings that preserve additional structure, for example, isometric embeddings of Riemannian manifolds or embeddings as symplectic or isotropic submanifolds into euclidean spaces with the standard Riemannian or symplectic structure. In this talk I will discuss some old and new problems concerning embeddings with special properties of complex or real manifolds into complex Euclidean spaces. We start with Stein manifolds and then discuss totally real embeddings and embeddings with special approximation properties. These problems have a topological component, such as Gromov's h-principle and Morse theory.

Colloquium

Speaker: Cristian Bravo Roman (Western)

"Are causal effects estimations the key to optimal recommendations under multi-treatment scenarios?"

Time: 15:30

Room: MC 107

Abstract: When making decisions that impact a specific context, it is essential to include a causal effect estimation analysis. This analysis allows us to compare potential outcomes under different treatment options or the control, aiding in selecting the best treatment option that leads to optimal results. However, merely estimating individual treatment effects may not suffice for making truly optimal decisions. To reveal this limitation, our study explores the incorporation of additional criteria, such as the uncertainty of these estimations, measured through a concept similar to the Conditional Value-at-Risk, commonly used in portfolio and insurance management. Additionally, we evaluate the inclusion of a specific prediction condition, particularly when the highest output is the desired outcome. With these intentions in mind, we propose a comprehensive methodology for multi-treatment selection, especially in situations where greater output is more desirable. Our suggested approach ensures the satisfaction of the overlap condition for comparing outcomes for treated and control groups. This involves training propensity score models as a preliminary step before employing traditional causal models — a crucial aspect often overlooked in other research. To illustrate the practical application of our methodology, we focus on the significant problem of credit card limit adjustment, which has historically been reliant on expert-driven choices. Analyzing historical data from a fintech company, we discovered that relying solely on counterfactual predictions is inadequate for generating appropriate credit line modifications. Instead, incorporating the two additional criteria significantly enhances the performance of the generated policy.

Short bio: Dr. Cristián Bravo is an Associate Professor and Canada Research Chair in Banking and Insurance Analytics at Western University, and Director of the Banking Analytics Lab. His research focuses on data science, analytics, and credit risk, particularly exploring multimodal deep learning, causal inference, and social network analysis to understand consumer-financial institution relations. With over 75 publications in prestigious journals and conferences, he contributes significantly to operational research, finance, and computer science. He frequently appears on CBC News’ Weekend Business Panel, and has been quoted by The Wall Street Journal, WIRED, CTV, The Toronto Star, The Globe and Mail, and Global News discussing topics in Banking, Finance, and Artificial Intelligence.

Graduate Seminar

Speaker: Esther Yartey (Western)

"Structural connectivity across datasets and species reveals community structure in cortex with specific connection features"

Time: 16:30

Room: MC 107

Advancements in neuroimaging technologies, particularly diffusion MRI, now allow reconstructing the long-range fiber connection patterns in the human brain. We study the network whose connection weights are determined by the number of fibers between individual brain regions. We study networks from the Human Connectome Project (HCP) and networks extracted from individual imaging subjects through a data processing pipeline developed in our group. By applying an algorithm to detect highly connected “communities” in these networks, we find a discrete set of communities appear robustly in the human brain. A specific community in the occipital lobe systematically displays high eigenvector centrality (EVC), a measure of the influence of nodes within a network. We explore the variations in these network structures among individuals and in retested subjects to isolate the sources of inter-individual variability. This result consistently appears across nearly all subjects and in a test-retest dataset. Similar community structure also appears in connectomes from macaque and marmoset brains, but the existence of an occipital lobe community with high EVC is specific to human connectomes. Taken together, these results reveal novel organization in the structural connectivity of the brain, derived from a fully data-driven approach, where clear community organization appears. This community organization relates to known functional divisions, such as visual and auditory sensory pathways, but also reveals community structure within higher-order areas, whose functional relevance can be studied in future work.

Transformation Groups Seminar

Speaker: Steven Amelotte (Western)

"Projective toric manifolds via symplectic reduction"

Time: 10:30

Room: MC 204

Algebraic Geometry

Speaker: Curtis Wilson (Western)

"The image of a polynomial map"

Time: 15:30

Room: MC 107

We recall the Zariski closure of an image, show that the image may not be the same as the Zariski closure, and ask what can be said about image of an affine variety under a polynomial map in general. We answer this question for the case V ⊂ Rn, and then prove that if K = C then the Zariski closure of the image coincides with the closure in the standard topology. Finally restricting our focus to regular maps, we show that the image of a projective variety in an algebraically closed field is Zariski closed and demonstrate some consequences of this result

Graduate Seminar

Speaker: Yunhai (Daniel) Xiang (Western)

"An easy tour of Galois cohomology"

Time: 16:30

Room: MC 107

Galois cohomology is a topic that should interest a wide range of audiences: number theorists, algebraic geometers, homotopy theorists, etc. It is a wonderful example of an application of ideas from algebraic topology to study algebra and number theory. In this talk, we will discuss the basics of Galois cohomology, and we demonstrate its power by using it to prove the Mordell-Weil theorem for elliptic curves. If time permits, we might also discuss a little bit about its generalization: étale cohomology.

Transformation Groups Seminar

Speaker: Matthias Franz (Western)

"The integral cohomology of smooth toric varieties"

Time: 10:30

Room: MC 204

We present a proof that the integral cohomology of a smooth toric variety is additively isomorphic to a torsion product involving the Stanley-Reisner ring of the fan defining the toric variety. Ingredients are a result of Gugenheim-May about the cohomology of pull-backs of principal torus bundles and a formality result for Davis-Januszkiewicz spaces.

Final Presentation

Speaker: Meagan James (Western)

"An Introduction to Mapping Class Groups"

Time: 13:30

Room: MC 108

Given a surface S, the set of all homeomorphisms from S to itself which fix the boundary and preserve orientation form a group under composition; this is known as the group of homeomorphisms and is denoted Homeo+(S, ∂S). The mapping class group of S, denoted Mod(S), can be understood as Homeo+(S, ∂S) modulo homotopy. Mapping class groups are often studied using simple closed curves in the surface, that is, embeddings of the form f : S1 → S. More specifically, given a collection of simple closed curves in S, we can understand the behaviour of an element of the mapping class group f ∈ Mod(S) by observing what happens to the simple closed curves after applying a representative homeomorphism ϕ of the class f to the surface S. The curve graph, denoted C(S), is a graph whose vertices correspond to isotopy classes of essential simple closed curves in S and edges join vertices whose isotopy classes have disjoint representatives. In this talk, we will become familiarized with curves in surfaces in order to better understand mapping class groups of different surfaces. We will then discuss the nature of the curve graph and how it can be used as a combinatorial model of Mod(S).

Geometry and Topology

Speaker: Luuk Stehouwer (Dalhousie University)

"Cutting and pasting manifolds"

Time: 15:30

Room: MC 107

In this talk, we will explore an equivalence relation on manifolds through cutting and pasting along boundaries. This relation leads to the definition of an abelian group known as the SKK-group, which was introduced by Karras, Kreck, Neumann, and Ossa in the 1970s. We will discuss the connection between the SKK-group and the bordism category, as well as the bordism group. This connection is made clearer through the examination of the fundamental group of the geometric realization of categories, described using zig-zags. Additionally, I will present joint work with Simona Veselá and Renee Hoekzema, where we compute the SKK groups for particular cases. If time allows, we will also briefly explore the relationship between the SKK-group and invertible topological quantum field theory.

Colloquium

Speaker: Ajneet Dhillon (Western)

"Basic Notions: The Borel-Bott-Weil theorem"

Time: 15:30

Room: MC 107

The Borel-Bott-Weil theorem describes the cohomology of line bundles on homogeneous varieties in terms of the representation theory linear algebraic groups. This talk will be a gentle introduction to this theorem in the case of the general linear group.

The first part of the talk will be an extensive motivation for why one is interested in line bundles on projective varieties and their cohomologies. In an nutshell, line bundles turn the extrinsic problem of studying maps to projective space into an intrinsic one.

The second part of the talk will discuss the representation theory of the general linear group and will end with a statement of the theorem in this special case.

Graduate Seminar

Speaker: Curtis Wilson (Western)

"The Golod-Shafarevich Theorem"

Time: 16:30

Room: MC 108

We introduce the class field tower infinite issue and state its solution, the Golod-Shafarevich theorem. We prove the theorem, and provide a refinement for the graded case. We discuss some examples and finish with an application involving finitely generated infinite torsion groups.