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Monday, February 23, 2026 2:45 pm - 3:45 pm EST (GMT -05:00)

Graphs and Matroids - Agnes Totschnig-Colouring graphs with forbidden 7-vertex minors

Speaker: Agnes Totschnig
Affiliation: McGill University
Room: MC 5479

Abstract:In 1943, Hadwiger conjectured that every k-chromatic graph has a K_k-minor. While the cases k = 5 and k = 6 have been shown to be equivalent to the Four Colour Theorem, respectively by Wagner, and in seminal work by Robertson, Seymour and Thomas, the cases k at least 7 remain open. We show that any 7-chromatic graph has as a minor the complete graph K_7 with two adjacent edges removed, by extending work of Kawarabayashi and Toft and by proving a new edge-extremal bound. This improves Jakobsen’s result with two arbitrary edges removed. Joint work with Sergey Norin.

Thursday, February 26, 2026 2:30 pm - 3:30 pm EST (GMT -05:00)

Algebraic & Enumerative Combinatorics - Adrien Segovia-The dimension of semidistributive extremal lattices

Speaker: Adrien Segovia
Affiliation: Université du Québec à Montréal
Location: MC 5417

Abstract: The order dimension of a partially ordered set (poset), which is often difficult to compute, is a measure of its complexity. Dilworth proved that the dimension of a distributive lattice is the width of its subposet on its join-irreducible elements. We generalize this result by showing that the dimension of a semidistributive extremal lattice is the chromatic number of the complement of its Galois graph (see Section 3.5 of arXiv:2511.18540). We apply this result to prove that the dimension of the lattice of torsion classes of a gentle tree with n vertices is equal to n. No advanced background is required to follow the talk.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm in MC 5417.

Friday, February 27, 2026 10:30 am - 11:30 am EST (GMT -05:00)

Crypto Reading Group - Jack Zhao-Post-Quantum PKE from Unstructured Noisy Linear Algebraic Assumptions: Beyond LWE and Alekhnovich’s LPN

Speaker:

 Jack Zhao
Affiliation: University of Waterloo
Location: MC 6029

Abstract: Much of post-quantum PKE from unstructured noisy linear algebra relies on LWE or Alekhnovich’s LPN: both assume samples of the form (A, As+e) are computationally indistinguishable from (A, u), but with different noise models. LWE uses “short” errors, while Alekhnovich LPN uses sparse errors. Motivated by uncertainty around future cryptanalytic advances, we ask whether one can still obtain PKE from noisy linear assumptions even if both LWE and Alekhnovich LPN were broken. We talk about two new assumptions: Learning with Two Errors (LW2E), which mixes an LWE-style short error with an LPN-style sparse error, and Learning with Short and Sparse Errors (LWSSE), which uses errors that are simultaneously short and sparse but denser than Alekhnovich LPN.
Thursday, March 19, 2026 2:30 pm - 3:30 pm EDT (GMT -04:00)

Algebraic and enumerative combinatorics seminar - Moriah Elkin- Open quiver loci, CSM classes, and chained generic pipe dreams

Speaker: Moriah Elkin
Affiliation: Cornell University
Location: MC 5417

Abstract: In the space of type A quiver representations, putting rank conditions on the maps cuts out subvarieties called "open quiver loci." These subvarieties are closed under the group action that changes bases in the vector spaces, so their closures define classes in equivariant cohomology, called "quiver polynomials." Knutson, Miller, and Shimozono found a pipe dream formula to compute these polynomials in 2006. To study the geometry of the open quiver loci themselves, we might instead compute "equivariant Chern-Schwartz-MacPherson classes," which interpolate between cohomology classes and Euler characteristic. I will introduce objects called "chained generic pipe dreams" that allow us to compute these CSM classes combinatorially, and along the way give streamlined formulas for quiver polynomials.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.