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27 Fields Special Presentation
Fields Special Presentation Speaker: Fields (University of Toronto) "Quantitative Information Security Specialist Program" Time: 14:30 - 15:30 Room: WSC 240 This training program is specifically designed for graduate students and recent PhDs in mathematics or related fields, who are looking to transition to work in the information security industry after graduation. Geometry and Combinatorics
Geometry and Combinatorics Speaker: Daniel Bath (KU Leuven) "Bernstein-Sato polynomials for hyperplane arrangements of rank 3" Time: 15:30 - 16:30 Room: MC 108 The Bernstein-Sato polynomial (and its roots) are important invariants of hypersurface singularities. It is a Rosetta Stone: it seems most singularity data lies within, if only one could decode it. Unfortunately, after 50 years actual computations remain scarce. I will give a formula for the roots of Bernstein-Sato polynomials of hyperplane arrangements in three variables. It turns out all but one root is determined by the combinatorics, and the outlier root is determined by simple algebraic data. Time permitting I will connect this non-combinatorial root to the realization space of the underlying matroid. |
28 Symplectic and Complex Geometry
Symplectic and Complex Geometry Speaker: Siyuan Yu (Western) "TBA" Time: 13:30 - 14:30 Room: MC 107 |
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30 Colloquium
Colloquium Speaker: Assaf Bar-Natan (Model six) "Big Surfaces, Medium Geometry, and Small Triangles" Time: 15:30 - 16:30 Room: MC 107 For a compact surface S, $MCG(S) = Homeo(S)/Homeo_0(S)$ is a group well-studied and loved by many, but especially by geometric group theorists because it is finitely generated, and hence has a coarse geometry coming from its Cayley graph. When S is big (infinite-type), $MCG(S)$ is Polish and no longer discrete, but following the work of Rosendal and Mann-Rafi, we can still define a coarse geometry and a Cayley graph. In ongoing work with Schaffer-Cohen—Verberne and Qing—Rafi, we can show that for some surfaces, $MCG(S)$ is non-elementary $\delta$-hyperbolic, and some have infinite coarse rank. If you like surfaces, geometry, topology, and Polish groups, come by! |
31 Algebra Seminar
Algebra Seminar Speaker: Mac Martin (Western) "TBA" Time: 14:30 - 15:30 Room: MC 108 TBA |
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12 Geometry and Topology
Geometry and Topology Speaker: Siyuan Yu (Western) "Symplectic embeddings of balls in $\mathbb{C}P^2$ and the generalized configuration space" Time: 15:30 - 16:20 Room: MC 107 \textbf{Abstract.}
Let \(\mathrm{IEmb}\!\big(B^{4}(c),\mathbb{C}P^{2}\big)\) denote the space of unparameterized symplectic embeddings of \(k\) balls of capacities \((c_{1},\dots,c_{k})\), where \(1\le k\le 8\).
It is known from the work of S.~Anjos, J.~Li, T.-J.~Li, and M.~Pinsonnault that the space of capacities decomposes into convex polygons called stability chambers, and that the homotopy type of \(\mathrm{IEmb}\!\big(B^{4}(c),\mathbb{C}P^{2}\big)\) depends solely on the stability chambers.
Based on recent results of M.~Entov and M.~Verbitsky on Kähler-type embeddings, we show that for \(1\le k\le 8\), \(\mathrm{IEmb}\!\big(B^{4}(c),\mathbb{C}P^{2}\big)\) is homotopy equivalent to a union of strata \(F_{I}\) of the configuration space of the complex projective plane \(F(\mathbb{C}P^{2},k)\).
The proof relies on constructing an explicit map from the space of K\"ahler-type embeddings to a generalized version of the configuration space that incorporates both configurations of points and compatible complex structures on \(\mathbb{C}P^{2}\).
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14 Transformation Groups Seminar
Transformation Groups Seminar Speaker: Kumar Shukla (Western) "Syzygies in Equivariant Cohomology of Toric Varieties" Time: 09:30 - 11:00 Room: MC 106 We will study the syzygy order of equivariant cohomology of toric varieties by the means of regular sequences on the piecewise polynomial algebra associated to the underlying fan. |
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18 Symplectic and Complex Geometry
Symplectic and Complex Geometry Speaker: Martin Pinsonnault (Western) "Flexible Stein and Weinstein structures" Time: 13:30 - 14:30 Room: MC 107 |
19 Colloquium
Colloquium Speaker: Emmy Murphy (Toronto) "Flexibility in contact and symplectic geometry" Time: 15:30 - 16:30 Room: MC 107 A Stein manifold is a complex manifold admitting a proper holomorphic embedding into C^n. Work of Cieliebak-Eliashberg (among others) fundamentally relates the geometry of Stein manifolds to their symplectic structures. This relationship gives rise to Weinstein handle decompositions, which allows us to study Stein manifolds via Legendrian knot theory in contact manifolds. This gives rise to new tools: the h-principles in contact geometry. We'll explain the motivation behind contact geometry, what the h-principle is, and how those topics tie together to influence the geometry of Stein manifolds, and cobordisms. |
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21 Algebra Seminar
Algebra Seminar Speaker: Elias Vandenberg (Western) "Tanaka Duality." Time: 14:30 - 15:30 Room: MC 108 |
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26 Geometry and Topology
Geometry and Topology Speaker: Herng Yi Cheng (Toronto) "Geometric representations of cohomology operations" Time: 15:30 - 16:20 Room: MC 107 Abstract: We will begin this talk by showing how to represent the cohomology of some spaces by geometrically nice maps to spaces of cycles on spheres. These maps may be viewed as analogues of differential forms. Moreover, maps between spaces of mod p cycles represent operations on mod p cohomology that generalize the cup product, such as the Steenrod squares and Steenrod powers. These operations are fundamental to certain methods for computing stable homotopy groups. We will present the first geometric construction of maps between spaces of cycles that represent mod p cohomology operations, with an eye towards applications in quantitative topology. (arXiv:2510.12574) |
27 Colloquium
Colloquium Speaker: Sita Gakkhar (University of Waterloo) "Probability and geometry in open quantum systems" Time: 14:00 - 15:00 Room: MC 107 We will show how to associate to the data of a noncommutative geometry an open quantum system which carries a natural quantum diffusion process. We will consider how this process generalizes the classical Laplacian generated diffusion. We will introduce needed ideas from noncommutative probability, and consider quantum analogs of the Feynman-Kac formulae which we apply to evaluating the spectral action. Finally we highlight some unexplored possibilities which are opened by this mixing of noncommutative probability and geometry.
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4 PhD Thesis Defence
PhD Thesis Defence Speaker: Shubhankar (Western) "TBA" Time: 13:30 - 14:30 Room: MC 204 Colloquium
Colloquium Speaker: Michael Borinsky (Perimeter Institute) "On the Euler characteristic of the commutative graph complex" Time: 15:30 - 16:30 Room: MC 107 The dark matter problem in the moduli space of curves is a question about the nature of its unstable cohomology: Huge amounts of unstable cohomology are known to exist due to an Euler characteristic computation by Harer and Zagier. However, there are almost no constructions for unstable classes. A theorem of Chan, Galatius and Payne uses Kontsevich's commutative graph complex to shed new light on this dark matter problem. I will explain how the asymptotic behaviour of the Euler characteristic of this graph complex gives new insights into the limits of Chan, Galatius and Payne's construction and provides a new dark matter problem for commutative graph homology. |
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