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DTSTART;TZID=America/Los_Angeles:20260407T121500
DTEND;TZID=America/Los_Angeles:20260407T131000
DTSTAMP:20260413T170115
CREATED:20260120T211724Z
LAST-MODIFIED:20260331T041748Z
UID:3963-1775564100-1775567400@colleges.claremont.edu
SUMMARY:Tropical linear series and matroids (Dagan Karp\, HMC)
DESCRIPTION:In this talk\, I’ll attempt to give a friendly introduction to tropical linear series and explore their relationship to matroid theory. Along the way\, we’ll stop to admire the beautiful view from enumerative geometry and combinatorics. This is joint work with Chih-Wei Chang\, Matthew Dupraz\, Hernan Iriarte\, David Jensen\, Sam Payne\, and Jidong Wang\, and also with Jenna Luo. 
URL:https://colleges.claremont.edu/ccms/event/antc-talk-dagan-karp-hmc-2/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20260331T121500
DTEND;TZID=America/Los_Angeles:20260331T131000
DTSTAMP:20260413T170115
CREATED:20260106T162953Z
LAST-MODIFIED:20260321T145212Z
UID:3941-1774959300-1774962600@colleges.claremont.edu
SUMMARY:Central moments of autocorrelation demerit factors of binary sequences (Daniel Katz\, CSUN)
DESCRIPTION:A low autocorrelation binary sequence of length $\ell$ is an $\ell$-tuple of $+1$s and $-1$s that does not strongly resemble any translate of itself.  Such sequences are used in communications and remote sensing for synchronization and ranging\, where translation represents time delay.  A single number that indicates how good a sequence is for such purposes\, called the merit factor\, was introduced by Golay.  Its reciprocal is the demerit factor\, which is more natural to analyze due to its connection with norms of polynomials on the complex unit circle.  We consider the uniform probability measure on the $2^\ell$ binary sequences of length $\ell$ and investigate the distribution of the demerit factors of these sequences.  Sarwate and Jedwab have respectively calculated the mean and variance of this distribution. For each positive integer $p$\, we derive a formula for the $p$th central moment of the demerit factor for the binary sequences of length $\ell$; this is $\ell^{-2 p}$ times a quasipolynomial function of $\ell$.  The derivations rely on new combinatorial techniques\, assisted by group theory and Ehrhart theory\, and show that all the central moments are strictly positive for $p\geq 2$ and $\ell \geq 4$. Jedwab’s formula for variance is confirmed\, and we go beyond previous results by also deriving an exact formula for the skewness (by hand) and for the kurtosis and the fifth moment (by computer).  We obtain asymptotic values for all central moments in the limit as the length $\ell$ of the sequences tends to infinity.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-daniel-katz-csun/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20260324T121500
DTEND;TZID=America/Los_Angeles:20260324T131000
DTSTAMP:20260413T170115
CREATED:20260209T235439Z
LAST-MODIFIED:20260226T211019Z
UID:3991-1774354500-1774357800@colleges.claremont.edu
SUMMARY:Computing certificates for complete positivity (Achill Schürmann\, University of Rostock)
DESCRIPTION:A key problem in computer proofs based on solutions from copositive optimization\, is checking whether or not a given quadratic form is completely positive or not. In this talk we describe the first known algorithm for arbitrary rational input. It is based on a suitable adaption of Voronoi’s Algorithm and the underlying theory from positive definite to copositive quadratic forms. We observe several similarities with the classical theory\, but also some differences\, in particular for three and more variables. A key element and currently the main bottleneck in our algorithm is an adapted shortest vector computation\, asking for all nonnegative integer vectors attaining the copositive minimum of a given copositive quadratic form. \n(based on joint work with Valentin Dannenberg\, Alexander Oertel\, Mathieu Dutour Sikiric and Frank Vallentin)
URL:https://colleges.claremont.edu/ccms/event/antc-talk-achill-schurmann-university-of-rostock/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20260310T123000
DTEND;TZID=America/Los_Angeles:20260310T131000
DTSTAMP:20260413T170115
CREATED:20260119T182717Z
LAST-MODIFIED:20260307T023545Z
UID:3961-1773145800-1773148200@colleges.claremont.edu
SUMMARY:Hecke algebras and motives (Robert Cass\, CMC)
DESCRIPTION:Hecke algebras play a central role in both number theory and representation theory. While some Hecke algebras have explicit descriptions in terms of generators and relations\, others are understood through structure constants that encode multiplicities in tensor products of representations. In this talk\, I will discuss several projects with Thibaud van den Hove and Jakob Scholbach aimed at using geometry and motives to give a uniform categorification of Hecke algebras. Along the way\, we will encounter the geometric Satake equivalence\, Gaitsgory’s central functor\, and Iwahori-Whittaker models.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-robert-cass-cmc-2/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20260303T121500
DTEND;TZID=America/Los_Angeles:20260303T131000
DTSTAMP:20260413T170115
CREATED:20260302T023221Z
LAST-MODIFIED:20260302T023221Z
UID:4013-1772540100-1772543400@colleges.claremont.edu
SUMMARY:On a new version of Siegel’s lemma  (Lenny Fukshansky\, CMC)
DESCRIPTION:The classical Siegel’s lemma (1929) asserts the existence of a nontrivial integer solution to an underdetermined integer homogeneous linear system\, whose “size” is small as compared to the size of the coefficients of the system. Far-reaching generalizations of this theorem\, producing a full basis for the solution space\, were obtained over number fields by Bombieri & Vaaler (1983)\, and over the field of algebraic numbers by Roy & Thunder (1996)\, where the “size” was measured by a height function. We obtain a new version of Siegel’s lemma\, bridging the Bombieri & Vaaler and Roy & Thunder results in two ways: (1) our basis lies over a fixed number field as in Bombieri & Vaaler’s theorem; (2) our height-bound does not depend on the number field in question as in Roy & Thunder’s theorem. Our result does not imply the previously established ones and is not implied by them\, and our basis has some additional interesting properties. Our method is quite different from the previous ones\, using only linear algebra. Joint work with Max Forst.
URL:https://colleges.claremont.edu/ccms/event/on-a-new-version-of-siegels-lemma-lenny-fukshansky-cmc/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20260217T121500
DTEND;TZID=America/Los_Angeles:20260217T131000
DTSTAMP:20260413T170115
CREATED:20260121T181315Z
LAST-MODIFIED:20260211T173037Z
UID:3964-1771330500-1771333800@colleges.claremont.edu
SUMMARY:Summer of Math Discovery: Two research projects on combinatorial polytopes (Andrés R. Vindas Meléndez\, HMC)
DESCRIPTION:This is a talk in two parts covering two projects that the speaker mentored over the summer of 2025. The first project deals with the study of polytopes that arise from the convex hulls of stack-sorting on particular permutations. The second project deals with the study of symmetric edge polytopes of a finite simple graph\, a centrally symmetric lattice polytope whose vertices are defined by the edges of the graph. Both projects studied the (Euclidean\, relative\, or normalized) volumes of the respective combinatorially defined polytope.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-andres-r-vindas-melendez-hmc/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20260203T121500
DTEND;TZID=America/Los_Angeles:20260203T131000
DTSTAMP:20260413T170115
CREATED:20260129T172206Z
LAST-MODIFIED:20260129T215939Z
UID:3977-1770120900-1770124200@colleges.claremont.edu
SUMMARY:Relationships between skein algebras (Helen Wong\, CMC)
DESCRIPTION:We will examine the multiplicative structure of two skein algebras— the usual Kauffman bracket skein algebra of a surface (generated by loops) and a generalization of it due to Roger-Yang (generated by loops and arcs).   In joint work with Chloe Marple\, we found a homomorphism between the usual skein algebra for a closed torus and the Roger-Yang skein algebra for a twice-punctured annulus.   In this talk\, I’ll present some ways we used that homomorphism to do computations\, and whether there might be similar relationships between skein algebras of other surfaces. 
URL:https://colleges.claremont.edu/ccms/event/antc-talk-helen-wong-cmc-2/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20260127T121500
DTEND;TZID=America/Los_Angeles:20260127T131000
DTSTAMP:20260413T170115
CREATED:20260106T213106Z
LAST-MODIFIED:20260106T233659Z
UID:3942-1769516100-1769519400@colleges.claremont.edu
SUMMARY:The forbidden quiver of a link (Sam Nelson\, CMC)
DESCRIPTION:Virtual links can be represented as equivalence classes of Gauss diagrams under Reidemeister moves. The Forbidden Moves are moves which look plausible but change the virtual isotopy class of the knot or link — indeed\, virtual knots are all trivial if we allow forbidden moves. However\, virtual links remain non-trivial. In this talk we show how to think of these links as quivers and in the process\, define several polynomial invariants of link homotopy. This is joint work with Stella Shah (Scripps College).
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-sam-nelson-cmc-4/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20251202T121500
DTEND;TZID=America/Los_Angeles:20251202T131000
DTSTAMP:20260413T170115
CREATED:20250808T202734Z
LAST-MODIFIED:20251120T202437Z
UID:3778-1764677700-1764681000@colleges.claremont.edu
SUMMARY:Positivity aspects of complete homogeneous symmetric polynomials (Stephan Garcia\, Pomona)
DESCRIPTION:Hunter’s theorem ensures that the complete homogeneous symmetric (CHS) polynomials of even degree are positive definite functions.  We provide new proofs of Hunter’s theorem\, applications to operator theory\, and a noncommutative (NC) generalization that sheds light even on the commutative case.  Surprisingly\, this work emerged from a problem in analytic combinatorics.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-stephan-garcia-pomona-2/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20251118T121500
DTEND;TZID=America/Los_Angeles:20251118T131000
DTSTAMP:20260413T170115
CREATED:20250808T232856Z
LAST-MODIFIED:20251113T200129Z
UID:3779-1763468100-1763471400@colleges.claremont.edu
SUMMARY:Non-vanishing of L-functions over function fields (Alexandra Florea\, UC Irvine)
DESCRIPTION:I will talk about some results concerning the non-vanishing of $L$-functions associated to fixed order characters $\ell$ at the central point over functions fields. Quadratic characters have been studied a lot over the years\, and very good non-vanishing results are available in this case\, due to work of Soundararajan. When focusing on cubic and higher order characters\, much less is known. In this talk\, I will explain how one can obtain a positive proportion of non-vanishing for any fixed order $\ell$ characters\, which goes to $0$ as $\ell$ goes to infinity. This is based on joint work with C. David and M. Lalin.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-alexandra-florea-uc-irvine/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20251111T121500
DTEND;TZID=America/Los_Angeles:20251111T131000
DTSTAMP:20260413T170115
CREATED:20250827T221608Z
LAST-MODIFIED:20251022T171318Z
UID:3799-1762863300-1762866600@colleges.claremont.edu
SUMMARY:Elementary probability via bundles (Wai Yan Pong\, Cal State Dominguez Hills)
DESCRIPTION:This talk explores elementary probability and statistics through the language of category theory. We introduce a category of Bundles and use it to reinterpret several results typically covered in an introductory course on probability and statistics. This approach naturally reveals the underlying geometric structures common to these results. The talk is accessible to anyone familiar with linear algebra\, and we hope teachers of probability will find this perspective fresh and interesting.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-wai-yan-pong-cal-state-dominguez-hills-2/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20251104T121500
DTEND;TZID=America/Los_Angeles:20251104T131000
DTSTAMP:20260413T170115
CREATED:20250818T205450Z
LAST-MODIFIED:20250824T043204Z
UID:3793-1762258500-1762261800@colleges.claremont.edu
SUMMARY:Classifying possible density degree sets of hyperelliptic curves (Jasmine Camero\, Emory University)
DESCRIPTION:Let $C$ be a nice (smooth\, projective\, geometrically integral) curve over a number field $k$. The single most important geometric invariant of a curve is the genus\, which can control various arithmetic properties of a curve. A celebrated result of Faltings implies that all points on $C$ come in families of bounded degree\, with finitely many exceptions. This result symbolized an advancement in the study of arithmetic information about curves and serves as the guiding philosophy of arithmetic geometry by highlighting the idea that “geometry governs arithmetic.” We explore the behavior of parameterized points and deduce consequences for the arithmetic of hyperelliptic curves\, specifically focusing on classifying the density degree sets of such curves.
URL:https://colleges.claremont.edu/ccms/event/classifying-possible-density-degree-sets-of-hyperelliptic-curves-jasmine-camero-emory-university/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20251028T121500
DTEND;TZID=America/Los_Angeles:20251028T131000
DTSTAMP:20260413T170115
CREATED:20250813T050114Z
LAST-MODIFIED:20251023T042930Z
UID:3784-1761653700-1761657000@colleges.claremont.edu
SUMMARY:From sparsity of rational points on curves to the generic positivity of Beilinson-Bloch height (Ziyang Gao\, UCLA)
DESCRIPTION:It is a fundamental question to find rational solutions to a given system of polynomials\, and in modern language this translates into finding rational points in algebraic varieties.  It is already very deep for algebraic curves defined over Q.  An intrinsic natural number associated with the curve\, called its genus\, plays an important role in studying rational points on curves.  In 1983\, Faltings proved the famous Mordell Conjecture (proposed in 1922)\, which asserts that any curve of genus at least 2 has only finitely many rational points.  Thus the problem for curves of genus at least 2 can be divided into several grades: finiteness\, bound\, uniform bound\, effectiveness.  An answer to each grade requires a better understanding of the distribution of the rational points.\n\nIn my talk\, I will explain the historical and recent developments of this problem according to the different grades.  I will also mention a recent work (joint with Shouwu Zhang) about a generic positivity property and a Northcott property of the Beilison-Bloch height of the Gross-Schoen cycles and the Ceresa cycles.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-ziyang-gao-ucla/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20251021T121500
DTEND;TZID=America/Los_Angeles:20251021T131000
DTSTAMP:20260413T170115
CREATED:20250807T222137Z
LAST-MODIFIED:20251007T213217Z
UID:3777-1761048900-1761052200@colleges.claremont.edu
SUMMARY:Singularities in characteristic p and the Riemann–Hilbert correspondence (Robert Cass\, CMC)
DESCRIPTION:The Riemann–Hilbert correspondence relates algebra to differential equations on complex algebraic varieties. In characteristic p\, there is an analogous correspondence due to Emerton–Kisin and later generalized by Bhatt–Lurie\, where the derivative operator is replaced by the p-th power Frobenius operator. In this talk we will explain a relation between the mod p Riemann–Hilbert correspondence and the study of singularities of algebraic varieties in characteristic p. This talk is mostly about commutative algebra\, and we will introduce concepts such as local cohomology and perverse sheaves along the way. This is joint work with João Lourenço.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-robert-cass-cmc/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20251007T121500
DTEND;TZID=America/Los_Angeles:20251007T131000
DTSTAMP:20260413T170115
CREATED:20250828T190015Z
LAST-MODIFIED:20250927T183316Z
UID:3800-1759839300-1759842600@colleges.claremont.edu
SUMMARY:The integer point transform as a complete invariant (Sinai Robins\, University of São Paulo\, Brazil)
DESCRIPTION:Given any finite set of integer points S\, there is an associated function f_S that encodes S\, which we call its integer point transform.   One can think of this integer point transform f_S algebraically or analytically.  Here we focus on its analytic properties\, showing that it is a complete invariant.   In fact\, we prove that it is only necessary to evaluate f_S at one algebraic point in order to uniquely determine the finite set S\, by employing the Lindemann-Weierstrass theorem.    Similarly\, we prove that it’s only necessary to evaluate the Fourier transform of a rational polytope P (as well as rational cones) at a single algebraic point\, in order to uniquely determine S.   Finally\, by relating the integer point transform to finite Fourier transforms\, we show that a finite number of integer point evaluations of f_S suffice in order to uniquely determine S.  
URL:https://colleges.claremont.edu/ccms/event/antc-talk-sinai-robins-university-of-sao-paulo-brazil/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20250930T121500
DTEND;TZID=America/Los_Angeles:20250930T131000
DTSTAMP:20260413T170115
CREATED:20250927T185625Z
LAST-MODIFIED:20250927T185625Z
UID:3874-1759234500-1759237800@colleges.claremont.edu
SUMMARY:Algebraic lattices and Pisot polynomials (Lenny Fukshansky\, CMC)
DESCRIPTION:A Z-module M in a number field K gives rise to a lattice in the corresponding Euclidean space via Minkowski embedding. Such lattices often carry inherited structure from the number field in question and can be attractive from both\, theoretical and applied perspectives. We consider this construction when M is spanned by the set of roots of an irreducible polynomial f(x) of prime degree n. In this case\, the resulting lattice has rank n or n-1 and includes the Galois group of f(x) as a subgroup of its automorphism group. Of particular interest is the case of Pisot polynomials\, i.e.\, polynomials with one positive real root and the rest of the roots in the unit circle. We construct infinite families of such polynomials of any prime degree for which the resulting lattices have bases of minimal vectors\, a property of interest in coding theory and cryptography applications. In case of the Galois group being cyclic\, A_n\, or S_n we derive formulas for the determinant of the lattice in terms of the symmetric functions of the roots of f(x). This is joint work with Evelyne Knight (Pomona College).
URL:https://colleges.claremont.edu/ccms/event/algebraic-lattices-and-pisot-polynomials-lenny-fukshansky-cmc/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20250923T121500
DTEND;TZID=America/Los_Angeles:20250923T131000
DTSTAMP:20260413T170115
CREATED:20250811T185820Z
LAST-MODIFIED:20250813T192625Z
UID:3783-1758629700-1758633000@colleges.claremont.edu
SUMMARY:Graphical designs: combinatorics and applications (Catherine Babecki\, Caltech)
DESCRIPTION:A graphical design is a quadrature rule for a graph inspired by classical numerical integration on the sphere. Broadly speaking\, that means a graphical design is a relatively small subset of graph vertices chosen to capture the global behavior of functions from the vertex set to the real numbers. We first motivate and define graphical designs for graphs with positive edge weights. Through Gale duality\, we exhibit a combinatorial bijection between graphical designs and the faces of certain polytopes associated to a graph\, called eigenpolytopes. This polytope connection implies a variety of beautiful consequences\, including a proof of existence\, an upper bound on the cardinality of a graphical design\, methods to compute\, optimize\, and organize graphical designs\, the existence of random walks with improved convergence rates\, and complexity results for associated computational problems.  We conclude with applications to the equitable facility location problem.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-catherine-babecki-caltech/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20250916T121500
DTEND;TZID=America/Los_Angeles:20250916T131000
DTSTAMP:20260413T170115
CREATED:20250809T192948Z
LAST-MODIFIED:20250811T173854Z
UID:3780-1758024900-1758028200@colleges.claremont.edu
SUMMARY:A non-uniformly inner amenable group (Isaac Goldbring\, UC Irvine)
DESCRIPTION:An inner amenable group is one in which there is a finitely additive conjugation-invariant probability measure on the non-identity elements.  In this talk\, we show that inner amenability is not preserved under elementary equivalence.  As a result\, we give the first example of a group that is inner amenable but not uniformly inner amenable.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-isaac-goldbring-uc-irvine/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20250902T121500
DTEND;TZID=America/Los_Angeles:20250902T131000
DTSTAMP:20260413T170115
CREATED:20250814T025232Z
LAST-MODIFIED:20250819T024559Z
UID:3787-1756815300-1756818600@colleges.claremont.edu
SUMMARY:Categorification of biquandle arrow weight invariants via quivers (Migiwa Sakurai\, Shibaura Institute of Technology)
DESCRIPTION:Biquandle arrow weights invariants are enhancements of the biquandle counting invariant for oriented virtual and classical knots defined from biquandle-colored Gauss diagrams using a tensor over an abelian group satisfying certain properties. In this talk\, we categorify the biquandle arrow weight polynomial invariant using biquandle coloring quivers\, obtaining new infinite families of polynomial invariants of oriented virtual and classical knots.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-migiwa-sakurai-shibaura-institute-of-technology/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20250422T121500
DTEND;TZID=America/Los_Angeles:20250422T131000
DTSTAMP:20260413T170115
CREATED:20250304T000158Z
LAST-MODIFIED:20250421T175544Z
UID:3727-1745324100-1745327400@colleges.claremont.edu
SUMMARY:Algebraic properties of linguistic structure (Isabella Senturia\, Yale / Caltech)
DESCRIPTION:The recognition that theoretical models of natural language syntax have robust algebraic foundations is longstanding. Both the syntactic structures proposed (trees\, semirings\, etc.) and metrics developed to understand them (the Chomsky hierarchy\, partial orders\, and so forth) closely resemble structures and systems familiar to theoretical mathematicians (groups\, rings\, fields\, …). Despite the underlying mathematical tools\, rarely do structural properties of language get analyzed at an algebraic level. I use two complementary perspectives\, one representational and continuous (spectral graph theory) and one derivational and discrete (Hopf algebras)\, as lenses to explore mathematical properties of linguistic structure. I will also show a connection between the two approaches through a case study on the problem of learning syntactic parameters.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-isabella-senturia-yale-caltech/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20250415T121500
DTEND;TZID=America/Los_Angeles:20250415T131000
DTSTAMP:20260413T170115
CREATED:20250226T050009Z
LAST-MODIFIED:20250413T154206Z
UID:3715-1744719300-1744722600@colleges.claremont.edu
SUMMARY:Jacobians of tropical curves and finite graphs (Carrie Frizzell\, Scripps)
DESCRIPTION:A Jacobian variety is a principally polarized abelian variety (PPAV) associated with a smooth complex algebraic curve. For dimensions less than or equal to 3\, every PPAV is either a Jacobian or a product of Jacobians. The Schottky problem concerns dimensions 4 and greater: which PPAVs are Jacobians? The Schottky problem can also be posed in the tropical setting\, in which the Jacobian of a tropical curve is a real torus. We will spend most of the talk discussing tropical Jacobians and their discrete counterparts\, but we will also survey a few results related to the aforementioned Schottky problem.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-carrie-frizzell-scripps/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20250408T121500
DTEND;TZID=America/Los_Angeles:20250408T131000
DTSTAMP:20260413T170115
CREATED:20250212T050525Z
LAST-MODIFIED:20250407T150550Z
UID:3692-1744114500-1744117800@colleges.claremont.edu
SUMMARY:The ANTC of ChatGPT: On the Mathematical Foundations of Large Language Models (Gizem Karaali\, Pomona)
DESCRIPTION:Large Language Models like ChatGPT rely on surprisingly familiar mathematics. This talk will explore how ideas from (linear) algebra\, number theory and combinatorics  appear — both directly and indirectly — in the structure and behavior of these models. Along the way\, we’ll touch on themes like structure\, symmetry\, and scale\, and consider how abstract mathematical ideas can shed light on systems that process and generate human language. The talk will be self-contained\, and no background in machine learning will be assumed. (This abstract was prepared with the assistance of ChatGPT\, which seems to be remarkably self-aware of its own mathematical foundations.)
URL:https://colleges.claremont.edu/ccms/event/antc-talk-gizem-karaali-pomona-3/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20250401T121500
DTEND;TZID=America/Los_Angeles:20250401T131000
DTSTAMP:20260413T170115
CREATED:20250206T191602Z
LAST-MODIFIED:20250326T164610Z
UID:3688-1743509700-1743513000@colleges.claremont.edu
SUMMARY:Permutation pattern avoidance\, alternating sign matrices\, and asymptotics (Justin Troyka\, Cal State LA)
DESCRIPTION:A big area in combinatorics over the last several decades has been the study of pattern-avoiding permutations\, whose enumeration is exciting and mysterious. Alternating sign matrices (ASMs) are a generalization of permutations whose study in combinatorics has also been exciting and mysterious. In this talk\, I will explain some new asymptotic results involving the number of ASMs that avoid a given permutation pattern\, from my joint work with Mathilde Bouvel\, Eric Egge\, Rebecca Smith\, and Jessica Striker. I will also show some of the highlights in the histories of both pattern-avoiding permutations and ASMs.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-justin-troyka-cal-state-la/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20250325T121500
DTEND;TZID=America/Los_Angeles:20250325T131000
DTSTAMP:20260413T170115
CREATED:20250127T201036Z
LAST-MODIFIED:20250324T151237Z
UID:3659-1742904900-1742908200@colleges.claremont.edu
SUMMARY:Some Diophantine analogies between Dirichlet series and polynomials (Vesselin Dimitrov\, Caltech)
DESCRIPTION:I will present an integral — requiring no character twists — converse theorem for recognizing when is a Dirichlet series with algebraic integer coefficients equal to the L-function of a modular form. This refines the unbounded denominators conjecture of Atkin and Swinnerton-Dyer. Analogies with basic function field arithmetic then suggest a quantitative refinement which precludes a pair of GL(2) automorphic L-functions with closely matched up zeros. I will explain how to get at such a theorem. 
URL:https://colleges.claremont.edu/ccms/event/antc-talk-vesselin-dimitrov-caltech/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20250302T121500
DTEND;TZID=America/Los_Angeles:20250304T131000
DTSTAMP:20260413T170115
CREATED:20250302T201628Z
LAST-MODIFIED:20250302T201628Z
UID:3716-1740917700-1741093800@colleges.claremont.edu
SUMMARY:Enumerative Invariants from Derived Categories III (Reginald Anderson\, CMC)
DESCRIPTION:We’ll first define the two-point gravitational correlators which appeared last week as descendant Gromov-Witten invariants. By request\, we’ll then introduce Gromov-Witten invariants as they appear in the expository work https://arxiv.org/abs/2501.03232 and give CP^1 to demonstrate some of the identities which GW invariants satisfy. If time allows\, we’ll also give the small and big quantum cohomology for CP^1.
URL:https://colleges.claremont.edu/ccms/event/enumerative-invariants-from-derived-categories-iii-reginald-anderson-cmc/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20250225T121500
DTEND;TZID=America/Los_Angeles:20250225T131000
DTSTAMP:20260413T170115
CREATED:20250218T192927Z
LAST-MODIFIED:20250218T193027Z
UID:3709-1740485700-1740489000@colleges.claremont.edu
SUMMARY:Enumerative invariants from derived categories -- part II (Reginald Anderson\, CMC)
DESCRIPTION:Following Kalashnikov\, we recover Givental’s small J function for CP^1 by viewing it as a quiver flag variety.
URL:https://colleges.claremont.edu/ccms/event/enumerative-invariants-from-derived-categories-part-ii-reginald-anderson-cmc/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20250218T121500
DTEND;TZID=America/Los_Angeles:20250218T131000
DTSTAMP:20260413T170115
CREATED:20250212T225636Z
LAST-MODIFIED:20250218T192952Z
UID:3696-1739880900-1739884200@colleges.claremont.edu
SUMMARY:Enumerative invariants from derived categories -- part I (Reginald Anderson\, CMC)
DESCRIPTION:Following Kalashnikov\, we recover Givental’s small J function for CP^1 by viewing it as a quiver flag variety.
URL:https://colleges.claremont.edu/ccms/event/enumerative-invariants-from-derived-categories-reginald-anderson-cmc/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20250211T121500
DTEND;TZID=America/Los_Angeles:20250211T131000
DTSTAMP:20260413T170115
CREATED:20250206T203702Z
LAST-MODIFIED:20250206T203729Z
UID:3689-1739276100-1739279400@colleges.claremont.edu
SUMMARY:On the illumination problem for convex sets (Lenny Fukshansky\, CMC)
DESCRIPTION:Let K be a compact convex set in the Euclidean space R^n. How many lights are needed to illuminate its boundary? A classical conjecture of Boltyanskii (1960) asserts that 2^n lights are sufficient to illuminate any such set K. While this is still open\, an earlier observation of Hadwiger (1945) guarantees that if K has smooth boundary\, then n+1 lights are sufficient: we only need to position these lights at the vertices of a simplex containing K in its interior. In fact\, this observation allows us to estimate how far from K these lights need to be. A more delicate problem arises if we insist on placing the lights at points of a fixed lattice L: how far from K must the lights be then? We discuss this problem\, producing a bound on this distance\, which depends on certain orthogonality and symmetry properties of the lattice in question. Interestingly\, for some nice classes of lattices\, a bound independent of L can be produced.
URL:https://colleges.claremont.edu/ccms/event/on-the-illumination-problem-for-convex-sets/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20250204T121500
DTEND;TZID=America/Los_Angeles:20250204T131000
DTSTAMP:20260413T170115
CREATED:20250123T065341Z
LAST-MODIFIED:20250123T065341Z
UID:3639-1738671300-1738674600@colleges.claremont.edu
SUMMARY:Quandle cohomology quiver representations (Sam Nelson\, CMC)
DESCRIPTION:Quandles are algebraic structures encoding the motion of knots through space. Quandle cocycle quivers categorify the quandle cocycle invariant. In this talk we will define a quiver representation associated to quandle cocycle quivers and use it to obtain new polynomial invariants of knots.
URL:https://colleges.claremont.edu/ccms/event/quandle-cohomology-quiver-representations-sam-nelson-cmc/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241203T121500
DTEND;TZID=America/Los_Angeles:20241203T131000
DTSTAMP:20260413T170115
CREATED:20240906T182729Z
LAST-MODIFIED:20241118T192728Z
UID:3497-1733228100-1733231400@colleges.claremont.edu
SUMMARY:Variations of oddtown and eventown (Jason O'Neill\, Cal State LA)
DESCRIPTION:The classical oddtown and eventown problems involve a collection of subsets of a finite set with an odd (resp. even) number of elements such that all pairwise intersections contain an even number of elements. In this talk\, we will discuss these results as well as the following variants: \n\nWe consider set sizes and pairwise intersection restrictions given modulo m as opposed to even/odd (mod 2).\nWe allow very “few” pairwise intersections in collections of subsets.\nWe impose further conditions on 3-wise and 4-wise intersections of our collection of subsets.\n\nAlong the way\, we will sprinkle in a few open problems.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-jason-oneill-cal-state-la/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
END:VCALENDAR