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Towers and elementary embeddings in total relatively hyperbolic groups (Christopher Perez, Loyola University New Orleans)

Davidson Lecture Hall, CMC 340 E 9th St, Claremont, CA, United States

In a remarkable series of papers Zlil Sela classified the first-order theories of free groups and torsion-free hyperbolic groups using geometric structures he called towers, and independently Olga Kharlampovich and Alexei Myasnikov did the same using equivalent structures they called regular NTQ groups. It was later proved by Chloé Perin that if H is an […]

Quantum money from Brandt operators (Shahed Sharif, CSU San Marcos)

Roberts North 102, CMC

Public key quantum money is a replacement for paper money which has cryptographic guarantees against counterfeiting. We propose a new idea for public key quantum money. In the abstract sense, our bills are encoded as a joint eigenstate of a fixed system of commuting unitary operators. We show that the proposal is secure against black […]

Numerical semigroups, minimal presentations, and posets (Chris O’Neill, SDSU)

Roberts North 102, CMC

A numerical semigroup is a subset S of the natural numbers that is closed under addition.  One of the primary attributes of interest in commutative algebra are the relations (or trades) between the generators of S; any particular choice of minimal trades is called a minimal presentation of S (this is equivalent to choosing a […]

Biquandle power brackets (Sam Nelson, CMC)

Roberts North 102, CMC

Biquandle brackets are skein invariants of biquandle-colored knots, with skein coefficients that are functions of the colors at a crossing. Biquandle power brackets take this idea a step further with state component values that also depend on biquandle colors. This is joint work with Neslihan Gügümcü (IYTE).

Chromatic numbers of abelian Cayley graphs (Michael Krebs, Cal State LA)

Roberts North 102, CMC

A classic problem in graph theory is to find the chromatic number of a given graph: that is, to find the smallest number of colors needed to assign every vertex a color such that whenever two vertices are adjacent, they receive different colors.  This problem has been studied for many families of graphs, including cube-like […]

Cellular resolutions of the diagonal and exceptional collections for toric D-M stacks (Reginald Anderson, CMC)

Roberts North 102, CMC

Beilinson gave a resolution of the diagonal for complex projective space, which gives a strong, full exceptional collection of line bundles as a generating set for the derived category of coherent sheaves. Bayer-Popescu-Sturmfels generalized Beilinson's resolution of the diagonal by giving a cellular resolution of the diagonal for a proper subclass of smooth toric varieties […]

Deep hole lattices and isogenies of elliptic curves (Lenny Fukshansky, CMC)

Roberts North 102, CMC

For a lattice L in the plane, we define the affiliated deep hole lattice H(L) to be spanned by a shortest vector of L and the furthest removed vector from the lattice contained in the triangle with sides corresponding to the shortest basis vectors. We study the geometric and arithmetic properties of deep hole lattices, […]

On the spectra of syntactic structures (Isabella Senturia, Yale University)

On Zoom

We explore the application of spectral graph theory to the problem of characterizing linguistically-significant classes of tree structures. We focus on various classes of syntactically-defined tree graphs, and show that the spectral properties of different matrix representations of these classes of trees provide insight into the linguistic properties that characterize these classes. More generally, our […]

Frobenius coin-exchange generating functions (Matthias Beck, San Francisco State University)

Roberts North 102, CMC

We study variants of the Frobenius coin-exchange problem: Given n positive relatively prime parameters, what is the largest integer that cannot be represented as a nonnegative integral linear combination of the given integers? This problem and its siblings can be understood through generating functions with 0/1 coefficients according to whether or not an integer is representable. […]

f^*-vectors of lattice polytopes (Max Hlavacek, Pomona College)

Roberts North 102, CMC

The Ehrhart polynomial of a lattice polytope P counts the number of integer points in the nth integral dilate of P. The f^* -vector of P, introduced by Felix Breuer in 2012, is the vector of coefficients of the Ehrhart polynomial with respect to the binomial coefficient basis . Similarly to h and h^* -vectors, […]

On the Cox ring of a weighted projective plane blown-up at a point (Javier Gonzalez Anaya, HMC)

Roberts North 102, CMC

The Cox ring of a projective variety is the ring of all its meromorphic functions, together with a grading of geometric origin. Determining whether this ring is finitely generated is a challenging task, even for simple examples. In this talk, we will discuss our efforts to tackle this problem for a specific class of varieties, […]

What can chicken nuggets tell us about symmetric functions, positive polynomials, random norms, and AF algebras? (Stephan Garcia, Pomona)

Roberts North 102, CMC

A simple question about chicken nuggets connects everything from analysis and combinatorics to probability theory and computer-aided design.  With tools from complex, harmonic, and functional analysis, probability theory, algebraic combinatorics, and spline theory, we answer many asymptotic questions about factorization lengths in numerical semigroups.  Our results yield uncannily accurate predictions, along with unexpected results about […]