12 events found.
Algebra / Number Theory / Combinatorics Seminar
Events
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Emmy Noether Room, Millikan 1021, Pomona College 610 N. College Ave., Claremont, California
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Representing integers by multilinear polynomials (Lenny Fukshansky, CMC)
On ZoomGiven a homogeneous multilinear polynomial F(x) in n variables with integer coefficients, we obtain some sufficient conditions for it to represent all the integers. Further, we derive effective results, establishing bounds on the size of a solution x to the equation F(x) = b, where b is any integer. For a special class of polynomials […]
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Region colorings in knot theory (Sam Nelson, CMC)
On ZoomIn this talk we will survey recent developments in the use of ternary algebraic structures known as Niebrzydowski Tribrackets in defining invariants of knots, with some perhaps surprising applications.
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On Hermite’s problem, Jacobi-Perron type algorithms, and Dirichlet groups (Oleg Karpenkov, Liverpool)
On ZoomIn this talk we introduce a new modification of the Jacobi-Perron algorithm in the three dimensional case. This algorithm is periodic for the case of totally-real conjugate cubic vectors. To the best of our knowledge this is the first Jacobi-Perron type algorithm for which the cubic periodicity is proven. This provides an answer in the […]
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The magic of the number three: three explanatory proofs in abstract algebra (Gizem Karaali, Pomona)
On ZoomWhen first learning how to write mathematical proofs, it is often easier for students to work with statements using the universal quantifier. Results that single out special cases might initially […]
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An algebraic introduction to the Kauffman bracket skein algebra (Helen Wong, CMC)
On ZoomThe Kauffman bracket skein algebra was originally defined as a generalization of the Jones polynomial for knots and links on a surface and is one of the few quantum invariants […]
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Critical points of toroidal Belyi maps (Edray Goins, Pomona)
On ZoomA Belyi map $\beta: \mathbb{P}^1(\mathbb{C}) \to \mathbb{P}^1(\mathbb{C})$ is a rational function with at most three critical values; we may assume these values are $\{ 0, \, 1, \, \infty \}$. Replacing $\mathbb{P}^1$ with an elliptic curve $E: \ y^2 = x^3 + A \, x + B$, there is a similar definition of a Belyi […]
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New norms on matrices induced by polynomials (Angel Chavez, Pomona)
On ZoomThe complete homogeneous symmetric (CHS) polynomials can be used to define a family of norms on Hermitian matrices. These 'CHS norms' are peculiar in the sense that they depend only on the […]
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Damerell’s theorem: p-adic version, supersingular case (Pavel Guerzhoy, University of Hawaii)
On ZoomIt is widely believed that Weierstrass ignored Eisenstein's theory of elliptic functions and developed an alternative treatment, which is now standard, because of a convergence issue. In particular, the Eisenstein […]
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Counting points in discrete subgroups (Jeff Vaaler, UT Austin)
On ZoomWe consider the problem of comparing the number of discrete points that belong to a set with the measure (or volume) of the set, under circumstances where we expect these […]
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The Chow ring of heavy/light Hassett spaces via tropical geometry (Dagan Karp, HMC)
On ZoomHassett spaces in genus 0 are moduli spaces of weighted pointed stable rational curves; they are important in the minimal model program and enumerative geometry. We compute the Chow ring […]
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On sparse representation of vectors in lattices and semigroups (Iskander Aliev, Cardiff University)
On ZoomWe will discuss the sparsity of the solutions to systems of linear Diophantine equations with and without non-negativity constraints. The sparsity of a solution vector is the number of its […]