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DTSTART;TZID=America/Los_Angeles:20251104T121500
DTEND;TZID=America/Los_Angeles:20251104T131000
DTSTAMP:20260421T095756
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:20260421T095756
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:20260421T095756
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:20260421T095756
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:20260421T095756
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:20260421T095756
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:20260421T095756
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:20260421T095756
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:20260421T095756
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:20260421T095756
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:20260421T095756
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:20260421T095756
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:20260421T095756
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:20260421T095756
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:20260421T095756
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:20260421T095756
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:20260421T095756
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:20260421T095756
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:20260421T095756
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
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241112T121500
DTEND;TZID=America/Los_Angeles:20241112T131000
DTSTAMP:20260421T095756
CREATED:20240118T205450Z
LAST-MODIFIED:20241028T192316Z
UID:3341-1731413700-1731417000@colleges.claremont.edu
SUMMARY:Traces of Partition Eisenstein series (Ken Ono\, University of Virginia)
DESCRIPTION:Integer partitions are ubiquitous in mathematics\, arising in subjects as disparate as algebraic combinatorics\, algebraic geometry\, number theory\, representation theory\, to mathematics physics. Many of the deepest results on partitions have their origin in the work of Ramanujan. In this lecture\, we will describe a completely new and unexpected role for partitions that also arises from the mysterious “lost notebook” of Ramanujan. We discover and explain the role of new q-series called “partition Eisenstein series”. These functions magically pop up as the key device for solving a conjecture of Andrews and Berndt\, for studying symmetric functions of 2-dimensional lattice sums\, for determining the properties of Andrews-Garvan “crank statistic”\, and for representing the Taylor coefficients of virtually every interesting Jacobi automorphic form. This talk will tell the story of the recent discovery of these functions\, and will offer a brief tour of these applications.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-ken-ono-university-of-virginia/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241105T121500
DTEND;TZID=America/Los_Angeles:20241105T131000
DTSTAMP:20260421T095756
CREATED:20240912T211317Z
LAST-MODIFIED:20241025T000409Z
UID:3512-1730808900-1730812200@colleges.claremont.edu
SUMMARY:Noether-Lefschetz theory and class groups (John Brevik\, Cal State Long Beach)
DESCRIPTION: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 behind Lefschetz’s proof\, I will sketch some of our recent progress in generalizing this theorem and its implications for global and local divisor class groups. We explore the question of what class groups are possible for local rings on surfaces in a particular analytic isomorphism class and show the ubiquitousness of unique factorization domains among such rings. Joint work with Scott Nollet (Texas Christian University).
URL:https://colleges.claremont.edu/ccms/event/antc-talk-john-brevik-cal-state-long-beach/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241029T121500
DTEND;TZID=America/Los_Angeles:20241029T131000
DTSTAMP:20260421T095756
CREATED:20240903T234219Z
LAST-MODIFIED:20241023T053311Z
UID:3487-1730204100-1730207400@colleges.claremont.edu
SUMMARY:Sequences with identical autocorrelation spectra (Daniel Katz\, Cal State Northridge)
DESCRIPTION: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.  We investigate the necessary and sufficient conditions for two sequences to be equicorrelational\, where\nwe take into consideration the alphabet from which their terms are drawn.  There are trivial forms of equicorrelationality arising from modifications that predictably preserve the autocorrelation\, for example\, negating the sequence or writing the sequence in reverse order and then complex conjugating every term.  By an exhaustive search of binary sequences up to length $44$\, we find that nontrivial equicorrelationality among binary sequences does occur\, but is rare.  We say that a positive integer $n$ is {\it unequivocal} to mean that there is no pair of nontrivially equicorrelational binary sequences of length $n$; otherwise $n$ is {\it equivocal}.  For integers $n \leq 44$\, we found that the unequivocal ones are $1$–$8$\, $10$\, $11$\, $13$\, $14$\, $19$\, $22$\, $23$\, $26$\, $29$\, $37$\, and $38$.  We prove that any multiple of a equivocal number is also equivocal\, and pose open questions as to whether there are finitely or infinitely many unequivocal numbers and whether the probability of nontrivial equicorrelationality occurring tends to zero as the sequence length tends to infinity.  (This is joint work with Adeebur Rahman and Michael J Ward.)
URL:https://colleges.claremont.edu/ccms/event/antc-talk-daniel-katz-cal-state-northridge-2/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241022T121500
DTEND;TZID=America/Los_Angeles:20241022T131000
DTSTAMP:20260421T095756
CREATED:20240909T190346Z
LAST-MODIFIED:20241016T201124Z
UID:3502-1729599300-1729602600@colleges.claremont.edu
SUMMARY:Making sandwiches: a novel invariant in D-module theory (David Lieberman\, HMC)
DESCRIPTION: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 an algebraic way of constructing the partial derivative.\n\nAn important result in the study of D-modules is Bernstein’s inequality\, first proved by Joseph Bernstein in the 1970’s. The result gives a lower bound on the filtered dimension of a D-module\, which a provide insights about modules of commutative algebras. The goal of this talk is to present some novel singular settings where this inequality holds. To do this\, we will introduce an invariant called sandwich Bernstein-Sato polynomials. These are analogous to a well studied object called the Bernstein-Sato polynomial\, which is a generalization of the power rule taught in undergraduate calculus courses. Using sandwich Bernstein-Sato polynomials\, we will show that Bernstein’s inequality holds true for the differential operators of the coordinate ring of the Segre product of projective spaces.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-david-lieberman-hmc/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241008T121500
DTEND;TZID=America/Los_Angeles:20241008T131000
DTSTAMP:20260421T095756
CREATED:20240901T163937Z
LAST-MODIFIED:20240929T202957Z
UID:3482-1728389700-1728393000@colleges.claremont.edu
SUMMARY:Counting matrix points via lattice zeta functions (Yifeng Huang\, USC)
DESCRIPTION:​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.)​.\n\nThe first problem is to count finite-field points on so called “varieties of matrix points”. They are created from a simple and fully elementary recipe and can yet easily get very complicated. The second problem is analogous to counting full-rank sublattices of $\mathbb{Z}^d$ with index $n$\, but with $\mathbb{Z}$ replaced by non-Dedekind rings\, such as non-maximal orders in number fields. (Containing joint work with Ken Ono\, Hasan Saad and joint work with Ruofan Jiang)
URL:https://colleges.claremont.edu/ccms/event/antc-talk-yifeng-huang-usc/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241001T121500
DTEND;TZID=America/Los_Angeles:20241001T131000
DTSTAMP:20260421T095756
CREATED:20240827T194511Z
LAST-MODIFIED:20241001T153641Z
UID:3473-1727784900-1727788200@colleges.claremont.edu
SUMMARY:Adinkras as Origami? (Edray Goins\, Pomona College)
DESCRIPTION: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 type of Dessin d’Enfant; they showed this by explicitly exhibiting a Belyi map as a composition $\beta: S \to \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C)$.  They computed the first arrow as a map from a certain compact connected Riemann surface $S$ to the Riemann sphere $\mathbb P^1(\mathbb C) \simeq S^2(\mathbb R)$\, and the second as a map which keeps track of the “coloring” of the edges.\n\nAdinkras naturally have square faces.  This keeps track of the non-commutative nature of the supersymmetric operators.  While Dessin d’Enfants correspond to triangular tilings of Riemann surfaces\, there is a similar construction — called “origami” — which correspond to square tilings.  In this project\, we attempt to discover how to express the construction of Doran\, et al. as a composition $\beta: S \to E(\mathbb C) \to \mathbb P^1(\mathbb C)$ for some elliptic curve elliptic curve $E$ such that the map corresponds to an “origami”\, that is\, a map which is branched over just one point.  This work is conducted as part of the Pomona Research in Mathematics Experience (DMS-2113782).
URL:https://colleges.claremont.edu/ccms/event/adinkras-as-origami-edray-goins-pomona-college/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240924T121500
DTEND;TZID=America/Los_Angeles:20240924T131000
DTSTAMP:20260421T095756
CREATED:20240825T022324Z
LAST-MODIFIED:20240825T022447Z
UID:3467-1727180100-1727183400@colleges.claremont.edu
SUMMARY:Presentations of derived categories (Reginald Anderson\, CMC)
DESCRIPTION: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 for toric subvarieties of smooth projective toric varieties. We give implications for exceptional collections on smooth projective toric Fano varieties in dimensions 1-4. This is joint work with CMC undergrads Justin Son\, Hill Zhang\, and Jumari Querimit-Ramirez.
URL:https://colleges.claremont.edu/ccms/event/localization-techniques-in-equivariant-cohomology-reginald-anderson-cmc/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240917T121500
DTEND;TZID=America/Los_Angeles:20240917T131000
DTSTAMP:20260421T095756
CREATED:20240824T183435Z
LAST-MODIFIED:20240906T183313Z
UID:3464-1726575300-1726578600@colleges.claremont.edu
SUMMARY:Biquandle module quiver representations (Sam Nelson\, CMC)
DESCRIPTION: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 invariants as decategorifications.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-sam-nelson-cmc-4/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240910T121500
DTEND;TZID=America/Los_Angeles:20240910T131000
DTSTAMP:20260421T095756
CREATED:20240825T022632Z
LAST-MODIFIED:20240906T182843Z
UID:3469-1725970500-1725973800@colleges.claremont.edu
SUMMARY:Localization techniques in equivariant cohomology (Reginald Anderson\, CMC)
DESCRIPTION: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 Euler characteristic by considering the torus-fixed loci; examples are given throughout.\n\nThe notes for this talk can be found here:\n\nhttps://drive.google.com/file/d/1FjhKDeJLIPQBlLA-x-BsnkosNayZMSAn/view?usp=sharing
URL:https://colleges.claremont.edu/ccms/event/localization-techniques-in-equivariant-cohomology-reginald-anderson-cmc-2/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240903T121500
DTEND;TZID=America/Los_Angeles:20240903T131000
DTSTAMP:20260421T095756
CREATED:20240824T184428Z
LAST-MODIFIED:20240824T184428Z
UID:3465-1725365700-1725369000@colleges.claremont.edu
SUMMARY:Lattice angles and quadratic forms (Lenny Fukshansky\, CMC)
DESCRIPTION: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? What if we designate a forbidden set of vectors\, what is the shortest y making a given angle with x outside of this forbidden set? It turns out that all of these questions can be reformulated in terms of a search for zeros of integral quadratic forms\, a rich arithmetic theory. We will give an introduction to this research direction and also show some of our recent results. Joint work with Sehun Jeong (CGU).
URL:https://colleges.claremont.edu/ccms/event/lattice-angles-and-quadratic-forms-lenny-fukshansky-cmc/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240430T121500
DTEND;TZID=America/Los_Angeles:20240430T131000
DTSTAMP:20260421T095756
CREATED:20240212T222657Z
LAST-MODIFIED:20240424T225203Z
UID:3383-1714479300-1714482600@colleges.claremont.edu
SUMMARY:Negligible cohomology (Matthew Gherman\, Caltech)
DESCRIPTION: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 and has deep connections with the embedding problem\, cohomological invariants\, and the profinite inverse Galois problem. Professor Alexander Merkurjev (UCLA) and I were able to compute negligible cohomology in degree 2\, compute the mod p negligible cohomology of elementary abelian p-groups\, and determine the Krull dimension of the quotient of mod p cohomology by the ideal of negligible elements.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-matthew-gherman-cal-tech/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
END:VCALENDAR