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Negligible cohomology (Matthew Gherman, Caltech)

Estella 2099

For a finite group G, a G-module M, and a field F, an element u in H^d(G,M) is negligible over F if for each field extension L/F and every continuous group homomorphism from Gal(L^{sep}/L) to G, u is in the kernel of the induced homomorphism H^d(G,M) to H^d(L,M). Negligible cohomology was first introduced by Serre […]

Lattice angles and quadratic forms (Lenny Fukshansky, CMC)

Estella 2099

What are the possible angles between two integer vectors in R^n? If we fix one such possible angle and one integer vector x, is there always another integer vector y that makes this angle with x? Assuming that x makes a given angle with some vector, how can we find the shortest such vector y? […]

Localization techniques in equivariant cohomology (Reginald Anderson, CMC)

Estella 2113

In order to understand a topological space X, it is often easier to understand X in terms of an action by a group G. When X is a compact complex manifold, we often let G be products of S^1 or \C^* acting in a nice way ("holomorphically") on X. This simplifies several calculations of an […]

Biquandle module quiver representations (Sam Nelson, CMC)

Estella 2113

Biquandle module enhancements are invariants of knots and links generalizing the classical Alexander module invariant. A quiver categorification of these invariants was introduced in 2020. In this work-in-progress (joint with Yewon Joung from Hanyang University in Seoul) we take the next step by defining invariant quiver representations. As an application we obtain new polynomial knot […]

Presentations of derived categories (Reginald Anderson, CMC)

Estella 2099

A modification of the cellular resolution of the diagonal given by Bayer-Popescu-Sturmfels gives a virtual resolution of the diagonal for smooth projective toric varieties and toric Deligne-Mumford stacks which are a global quotient of a smooth projective variety by a finite abelian group. In the past year, Hanlon-Hicks-Lazarev gave a minimal resolution of the diagonal […]

Adinkras as Origami? (Edray Goins, Pomona College)

Estella 2113

Around 20 years ago, physicists Michael Faux and Jim Gates invented Adinkras as a way to better understand Supersymmetry.  These are bipartite graphs whose vertices represent bosons and fermions and whose edges represent operators which relate the particles.  Recently, Charles Doran, Kevin Iga, Jordan Kostiuk, Greg Landweber and Stefan M\'{e}ndez-Diez determined that Adinkras are a […]

Counting matrix points via lattice zeta functions (Yifeng Huang, USC)

Estella 2113

​I will introduce two general problems and explain how they surprisingly connect with each other and with other aspects of mathematics (for a glimpse, Sato—Tate, hypergeometric functions, moduli spaces of sheaves, Catalan numbers, Hall polynomials, etc.)​. The first problem is to count finite-field points on so called "varieties of matrix points''. They are created from […]

Making sandwiches: a novel invariant in D-module theory (David Lieberman, HMC)

Estella 2113

In the field of commutative algebra, the principal object of study is (unsurprisingly) commutative algebras. A somewhat unintuitive fact is that results about commutative algebras can be gleaned from an associated non-commutative algebra whose generators are very analytic in nature. This object is called the ring of differential operators, often denoted by D. In a sense gives […]

Sequences with identical autocorrelation spectra (Daniel Katz, Cal State Northridge)

Estella 2113

In this talk, we explore sequences and their autocorrelation functions. Knowing the autocorrelation function of a sequence is equivalent to knowing the magnitude of its Fourier transform.  Resolving the lack of phase information is called the phase problem.  We say that two sequences are equicorrelational to mean that they have the same aperiodic autocorrelation function.  […]

Noether-Lefschetz theory and class groups (John Brevik, Cal State Long Beach)

Estella 2113

The classical Noether-Lefschetz Theorem states that a suitably general algebraic surface S of degree d ≥ 4 in complex projective 3-space P3 contains no curves besides complete intersections, that is, curves of the form S ∩ T where T is another surface. After discussing briefly Noether’s non-proof of this theorem and hinting at the idea […]