Deep hole lattices and isogenies of elliptic curves (Lenny Fukshansky, 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 […]
12 events found.
Algebra / Number Theory / Combinatorics Seminar
Events
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Roberts North 102, CMC
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On the spectra of syntactic structures (Isabella Senturia, Yale University)
On ZoomWe 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 […]
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Frobenius coin-exchange generating functions (Matthias Beck, San Francisco State University)
Roberts North 102, CMCWe 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 […]
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f^*-vectors of lattice polytopes (Max Hlavacek, Pomona College)
Roberts North 102, CMCThe 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 […]
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On the Cox ring of a weighted projective plane blown-up at a point (Javier Gonzalez Anaya, HMC)
Roberts North 102, CMCThe 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 […]
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What can chicken nuggets tell us about symmetric functions, positive polynomials, random norms, and AF algebras? (Stephan Garcia, Pomona)
Roberts North 102, CMCA 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, […]
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Skein algebra of a punctured surface (Helen Wong, CMC)
Roberts North 102, CMCThe Kauffman bracket skein algebra of a surface is at once related to quantum topology and to hyperbolic geometry. In this talk, we consider a generalization of the skein algebra […]
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Using quantum statistical mechanical systems to study real quadratic fields (Jane Panangaden, Pitzer College)
Estella 2099The original Bost-Connes system was constructed in 1990 and is a QSM system with deep connections to the field of rationals. In particular, its partition function is the Riemann-zeta function […]
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Quiver categorification of quandle invariants (Sam Nelson, CMC)
Estella 2099Quiver structures are naturally associated to subsets of the endomorphism sets of quandles and other knot-coloring structures, providing a natural form of categorification of homset invariants and their enhancements. In […]
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Point-counting and topology of algebraic varieties (Siddarth Kannan, UCLA)
Estella 2099A projective algebraic variety X is the zero locus of a collection of homogeneous polynomials, in projective space. When the polynomials have integer coefficients, we can think of the k-valued […]
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The restricted variable Kakeya problem (Pete Clark, University of Georgia)
Estella 2099For a finite field F_q, a subset of F_q^N is a Kakeya set if it contains a line in every direction (i.e., a coset of every one-dimensional linear subspace). The finite […]
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Homological mirror symmetry, curve counting, and a classical example: 27 lines on a nonsingular cubic surface (Reggie Anderson, CMC)
Estella 2099Though mirror symmetry requires much technical background, it gained traction in the mathematical community when physicists Candelas-de la Ossa-Green-Parkes discovered enumerative invariants counting the number of rational degree d curves […]