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DTSTART;TZID=America/Los_Angeles:20231031T121500
DTEND;TZID=America/Los_Angeles:20231031T131000
DTSTAMP:20260501T100143
CREATED:20230921T041133Z
LAST-MODIFIED:20231013T160601Z
UID:3248-1698754500-1698757800@colleges.claremont.edu
SUMMARY:On the spectra of syntactic structures (Isabella Senturia\, Yale University)
DESCRIPTION: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 goal is to provide another route to understanding the mathematical structure of natural language\, one that does not come from extensive definitions and rules defined via linguistic extrapolation\, but instead is extracted directly from computation on the syntactically-defined graphical structures.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-via-zoom-isabella-senturia-yale-university/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20231024T121500
DTEND;TZID=America/Los_Angeles:20231024T131000
DTSTAMP:20260501T100143
CREATED:20231003T045008Z
LAST-MODIFIED:20231003T234122Z
UID:3269-1698149700-1698153000@colleges.claremont.edu
SUMMARY:Deep hole lattices and isogenies of elliptic curves (Lenny Fukshansky\, CMC)
DESCRIPTION: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\, which turn out to be quite interesting. In particular\, we construct sequences of deep hole lattices corresponding to elliptic curves over a fixed number field. In the case of CM elliptic curves\, we prove that all elliptic curves generated by this sequence are isogenous to each other and produce bounds on the degree of isogeny. Finally\, we produce a counting estimate for the planar lattices with a prescribed deep hole lattice. Joint work with Pavel Guerzhoy and Tanis Nielsen.
URL:https://colleges.claremont.edu/ccms/event/deep-hole-lattices-and-isogenies-of-elliptic-curves-lenny-fukshansky-cmc/
LOCATION:Roberts North 102\, CMC
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20231003T121500
DTEND;TZID=America/Los_Angeles:20231003T131000
DTSTAMP:20260501T100143
CREATED:20230901T053808Z
LAST-MODIFIED:20230901T053808Z
UID:3170-1696335300-1696338600@colleges.claremont.edu
SUMMARY:Cellular resolutions of the diagonal and exceptional collections for toric D-M stacks (Reginald Anderson\, CMC)
DESCRIPTION: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 which they called “unimodular.” In joint work with Gabe Kerr\, we extended this resolution of the diagonal to smooth projective toric varieties by showing that the cokernel of Bayer-Popescu-Sturmfels’ resolution is torsion with respect to the irrelevant ideal. In this talk\, we show that Bayer-Popescu-Sturmfels’ resolution yields a strong\, full\, exceptional collection of line bundles for unimodular projective toric surfaces\, and that our extended resolution of the diagonal yields a strong\, full exceptional collection of line bundles for a smooth\, non-unimodular projective toric surface.
URL:https://colleges.claremont.edu/ccms/event/cellular-resolutions-of-the-diagonal-and-exceptional-collections-for-toric-d-m-stacks-reginald-anderson-cmc/
LOCATION:Roberts North 102\, CMC
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20230926T121500
DTEND;TZID=America/Los_Angeles:20230926T131000
DTSTAMP:20260501T100143
CREATED:20230828T163632Z
LAST-MODIFIED:20230828T211001Z
UID:3153-1695730500-1695733800@colleges.claremont.edu
SUMMARY:Chromatic numbers of abelian Cayley graphs (Michael Krebs\, Cal State LA)
DESCRIPTION: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 graphs\, unit-distance graphs\, circulant graphs\, integer distance graphs\, Paley graphs\, unit-quadrance graphs\, etc.  All of those examples just listed can be regarded as “abelian Cayley graphs\,” that is\, Cayley graphs whose underlying group is abelian.  Our goal is to create a unified\, systematic approach for dealing with problems of this sort\, rather than attacking each individually with ad hoc methods.  Building upon the work of Heuberger\, we associate an integer matrix to each abelian Cayley graph.  In certain cases\, such as when the matrix is small enough\, we can more or less read the chromatic number directly from the entries of the matrix.  In this way we immediately recover both Payan’s theorem (that cubelike graphs cannot have chromatic number 4) as well as Zhu’s theorem (which determines the chromatic number of six-valent integer distance graphs).  The proofs utilize only elementary group theory\, elementary graph theory\, elementary number theory\, and elementary linear algebra.  This is joint work with J. Cervantes.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-michael-krebs-cal-state-la/
LOCATION:Roberts North 102\, CMC
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20230919T121500
DTEND;TZID=America/Los_Angeles:20230919T131000
DTSTAMP:20260501T100143
CREATED:20230830T200520Z
LAST-MODIFIED:20230830T203839Z
UID:3165-1695125700-1695129000@colleges.claremont.edu
SUMMARY:Biquandle power brackets (Sam Nelson\, CMC)
DESCRIPTION: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).
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-sam-nelson-cmc-2/
LOCATION:Roberts North 102\, CMC
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20230912T121500
DTEND;TZID=America/Los_Angeles:20230912T131000
DTSTAMP:20260501T100143
CREATED:20230824T161426Z
LAST-MODIFIED:20230824T161426Z
UID:3146-1694520900-1694524200@colleges.claremont.edu
SUMMARY:Numerical semigroups\, minimal presentations\, and posets (Chris O'Neill\, SDSU)
DESCRIPTION: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 minimal binomial generating set for the defining toric ideal of S).  In this talk\, we present a method of constructing a minimal presentation of S from a portion of its divisibility poset.  Time permitting\, we will explore connections to polyhedral geometry.\n\nNo familiarity with numerical semigroups or toric ideals will be assumed for this talk.
URL:https://colleges.claremont.edu/ccms/event/numerical-semigroups-minimal-presentations-and-posets-chris-oneill-sdsu/
LOCATION:Roberts North 102\, CMC
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20230905T121500
DTEND;TZID=America/Los_Angeles:20230905T130500
DTSTAMP:20260501T100143
CREATED:20230415T215315Z
LAST-MODIFIED:20230830T150027Z
UID:3129-1693916100-1693919100@colleges.claremont.edu
SUMMARY:Quantum money from Brandt operators (Shahed Sharif\, CSU San Marcos)
DESCRIPTION: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 box attacks. In order to instantiate this protocol\, one needs to find a cryptographically complicated system of computable\, commuting\, unitary operators. To fill this need\, we propose using Brandt operators\, which have a beautiful tripartite formulation. No prior knowledge of quantum computers is necessary for this talk! This is joint work with Daniel Kane and Alice Silverberg.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-shahed-sharif-csu-san-marcos/
LOCATION:Roberts North 102\, CMC
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20230502T121500
DTEND;TZID=America/Los_Angeles:20230502T131000
DTSTAMP:20260501T100143
CREATED:20230125T224231Z
LAST-MODIFIED:20230425T203617Z
UID:3055-1683029700-1683033000@colleges.claremont.edu
SUMMARY:Towers and elementary embeddings in total relatively hyperbolic groups (Christopher Perez\, Loyola University New Orleans)
DESCRIPTION: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 elementarily embedded subgroup (or elementary submodel) of a torsion-free hyperbolic group G\, then G is a tower over H. We prove a generalization of Perin’s result to toral relatively hyperbolic groups using JSJ and shortening techniques.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-christopher-perez-loyola-university-new-orleans/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20230425T121500
DTEND;TZID=America/Los_Angeles:20230425T131000
DTSTAMP:20260501T100143
CREATED:20230116T180753Z
LAST-MODIFIED:20230417T230547Z
UID:3027-1682424900-1682428200@colleges.claremont.edu
SUMMARY:Bias in cubic Gauss sums: Patterson's conjecture (Alex Dunn\, CalTech)
DESCRIPTION:We prove\, in this joint work with Maksym Radziwill\, a 1978 conjecture of S. Patterson (conditional on the Generalized Riemann Hypothesis) concerning the bias of cubic Gauss sums. This explains a well-known numerical bias in the distribution of cubic Gauss sums first observed by Kummer in 1846. One important byproduct of our proof is that we show Heath-Brown’s cubic large sieve is sharp under GRH.  This disproves the popular belief that the cubic large sieve can be improved. An important ingredient in our proof is a dispersion estimate for cubic Gauss sums. It can be interpreted as a cubic large sieve with correction by a non-trivial asymptotic main term.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-alex-dunn-caltech/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20230418T121500
DTEND;TZID=America/Los_Angeles:20230418T131000
DTSTAMP:20260501T100143
CREATED:20230211T054504Z
LAST-MODIFIED:20230411T184945Z
UID:3078-1681820100-1681823400@colleges.claremont.edu
SUMMARY:Systems of homogeneous polynomials over finite fields with maximum number of common zeros (Sudhir Ghorpade\, IIT Bombay)
DESCRIPTION:It is elementary and well known that a nonzero polynomial in one variable of degree d with coefficients in a field F has at most d zeros in F. It is meaningful to ask similar questions for systems of several polynomials in several variables of a fixed degree\, provided the base field F is finite. These questions become particularly interesting and challenging when one restricts to polynomials that are homogeneous\, and considers zeros (other than the origin) that are non-proportional to each other. More precisely\, we consider the following question: \nGiven a system of a fixed number of linearly independent homogeneous polynomial equations of a fixed degree with coefficients in a fixed finite field F\, what is the maximum number of common zeros they can have in the corresponding protective space over F?The case of a single homogeneous polynomial (or in geometric terms\, a projective hypersurface) corresponds to a classical inequality proved by Serre in 1989. For the general case\, an elaborate conjecture was made by Tsfasman and Boguslavsky\, which was open for almost two decades. Recently significant progress in this direction has been made\, and it is shown that while the Tsfasman-Boguslavsky Conjecture is true in certain cases\, it can be false in general. Some new conjectures have also been proposed. We will give a motivated outline of these developments. If there is time and interest\, connections to coding theory or to the problem of counting points of sections of Veronese varieties by linear subvarieties of a fixed dimension will also be outlined. \nThis talk is mainly based on joint works with Mrinmoy Datta and with Peter Beelen and Mrinmoy Datta.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-sudhir-ghorpade-iit-bombay/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20230411T121500
DTEND;TZID=America/Los_Angeles:20230411T131000
DTSTAMP:20260501T100143
CREATED:20230201T212937Z
LAST-MODIFIED:20230405T034512Z
UID:3063-1681215300-1681218600@colleges.claremont.edu
SUMMARY:Discrete Calculus through generating functions (Wai Yan Pong\, Cal State Dominguez Hills)
DESCRIPTION:Discrete Calculus studies discrete structures\, such as sequences and graphs\, using techniques similar to those used in Calculus for continuous functions. The basic idea of generating functions is to associate a function with a sequence so that the coefficients of the power series expansion of the function represent the terms of the sequence. They provide a systematic way to encode information about a sequence or a combinatorial structure in a single function\, which can then be manipulated algebraically to obtain various types of results. In this talk\, we will examine a few well-known results about binomial coefficients\, Stirling numbers and Bernoulli numbers using both Discrete Calculus and generating functions as well as the interaction between them.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-wai-yan-pong-cal-state-dominguez-hills/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20230404T121500
DTEND;TZID=America/Los_Angeles:20230404T131000
DTSTAMP:20260501T100143
CREATED:20230112T225942Z
LAST-MODIFIED:20230327T230516Z
UID:3023-1680610500-1680613800@colleges.claremont.edu
SUMMARY:Noise stability of ranked choice voting (Steven Heilman\, USC)
DESCRIPTION:Given votes for candidates\, what is the best way to determine the winner of the election\, if some of the votes have been corrupted or miscounted?  As we saw in Florida in 2000\, where a difference of 537 votes determined the president of the United States\, the electoral college system does not seem to be the best voting method. We will survey some recent progress on the above question along with some open problems. In particular\, we consider which ranked choice voting method is most stable to corrupted or miscounted votes. \nhttps://arxiv.org/abs/2209.11183
URL:https://colleges.claremont.edu/ccms/event/antc-talk-steven-heilman-usc/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20230328T121500
DTEND;TZID=America/Los_Angeles:20230328T131000
DTSTAMP:20260501T100143
CREATED:20230124T212708Z
LAST-MODIFIED:20230320T225330Z
UID:3054-1680005700-1680009000@colleges.claremont.edu
SUMMARY:The Smith normal form of a polynomial of a random integral matrix (Gilyoung Cheong\, UC Irvine)
DESCRIPTION:Given a prime p\, let P(t) be a non-constant monic polynomial in t over the ring of p-adic integers. Let X(n) be an n x n uniformly random (0\,1)-matrix over the same ring. We compute the asymptotic distribution of the cokernel of P(X(n)) as n goes to infinity. When P(t) is square-free modulo p\, this lets us compute the asymptotic distribution of the Smith normal form of P(X(n)). In fact\, we shall consider the same problem with a more general random matrix X(n)\, which also includes the example of a Haar-random matrix. Our work crucially uses a recent work of W. Sawin and M. M. Wood which shows that the moments of finite size modules over any ring determine their distribution.\n\nThis is joint work with Myungjun Yu. https://arxiv.org/abs/2303.09125
URL:https://colleges.claremont.edu/ccms/event/antc-talk-gilyoung-cheong-uci/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20230321T121500
DTEND;TZID=America/Los_Angeles:20230321T131000
DTSTAMP:20260501T100143
CREATED:20230113T153459Z
LAST-MODIFIED:20230313T193754Z
UID:3025-1679400900-1679404200@colleges.claremont.edu
SUMMARY:Robust properties of graphs (Asaf Ferber\, UC Irvine)
DESCRIPTION:In this talk we will consider some notions of `robustness’ of graph/hypergraph properties. We will survey some existing results and will try to emphasize the following new result (joint with Adva Mond and Kaarel Haenni): The binomial random digraph $D_{n\,p}$ typically contains the minimum between the minimum out- and in-degrees many edge-disjoint Hamilton cycles\, given that $p\geq \log^C n/n$. The result is optimal up to log factors.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-asaf-ferber-uc-irvine/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20230221T121500
DTEND;TZID=America/Los_Angeles:20230221T131000
DTSTAMP:20260501T100143
CREATED:20230201T215846Z
LAST-MODIFIED:20230215T012913Z
UID:3065-1676981700-1676985000@colleges.claremont.edu
SUMMARY:On zeros of multilinear polynomials (Max Forst\, CGU)
DESCRIPTION:Consider rational polynomials in multiple variables that are linear with respect to some of the variables. In this talk we discuss the problem of finding a zero of such polynomials that are bounded with respect to a height function. For a system of such polynomials satisfying certain technical conditions we prove the existence of a bounded height simultaneous zero. For a single such polynomial we prove the existence of a zero of bounded height lying outside of a prescribed algebraic set. Based on joint work with Lenny Fukshansky.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-max-forst-cgu-2/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20230207T121500
DTEND;TZID=America/Los_Angeles:20230207T131000
DTSTAMP:20260501T100143
CREATED:20230202T190817Z
LAST-MODIFIED:20230202T190817Z
UID:3066-1675772100-1675775400@colleges.claremont.edu
SUMMARY:Orthogonality defect and coherence of cyclotomic lattices (Lenny Fukshansky\, CMC)
DESCRIPTION:There are two different measures of how far a given Euclidean lattice is from being orthogonal — the orthogonality defect and the average coherence. The first of these comes from the study of sphere packing while the second is motivated by frame theory\, but both of them have applications in digital communications\, especially in coding theory and cryptography. It is interesting to understand how the two are related. We investigate this question on an important class of cyclotomic lattices\, where some nice formulas can be derived and certain empirical observations can be made. Joint work with David Kogan.
URL:https://colleges.claremont.edu/ccms/event/orthogonality-defect-and-coherence-of-cyclotomic-lattices-lenny-fukshansky-cmc/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20230131T121500
DTEND;TZID=America/Los_Angeles:20230131T131000
DTSTAMP:20260501T100143
CREATED:20230112T013416Z
LAST-MODIFIED:20230112T054807Z
UID:3021-1675167300-1675170600@colleges.claremont.edu
SUMMARY:Biquandle arrow weights (Sam Nelson\, CMC)
DESCRIPTION:Many knot invariants are defined from features of knot projections such as arcs or crossings. Gauss diagrams provide an alternative combinatorial scheme for representing knots. In this talk we will use Gauss diagrams to enhance the biquandle counting invariant for classical and virual knots using biquandle arrow weights\, a new algebraic structure without a clear geometric interpretation. This is joint work with Migiwa Sakurai (Shibaura Institute of Technology\, Tokyo).
URL:https://colleges.claremont.edu/ccms/event/antc-talk-sam-nelson-cmc-3/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20221206T121500
DTEND;TZID=America/Los_Angeles:20221206T131000
DTSTAMP:20260501T100143
CREATED:20221130T053013Z
LAST-MODIFIED:20221130T053013Z
UID:3005-1670328900-1670332200@colleges.claremont.edu
SUMMARY:Positive semigroups in lattices and totally real number fields (Lenny Fukshansky\, CMC)
DESCRIPTION:Let  L be a full-rank lattice in R^n and write L+ for the semigroup of all vectors with nonnegative coordinates in L. We call a basis X for L positive if it is contained in L+. There are infinitely many such bases\, and each of them spans a conical semigroup S(X) consisting of all nonnegative integer linear combinations of the vectors of X. Such S(X) is a sub-semigroup of L+\, and we investigate the distribution of the gaps of S(X) in L+\, i.e. points in L+ outside of S(X). We describe some basic properties and counting estimates for these gaps. Our main focus is on the restrictive successive minima of these sets\, for which we produce bounds in the spirit of Minkowski’s successive minima theorem. We apply these results to obtain analogous bounds for the successive minima with respect to Weil height of totally positive sub-semigroups of ideals in totally real number fields. Joint work with Siki Wang (CMC’22).
URL:https://colleges.claremont.edu/ccms/event/positive-semigroups-in-lattices-and-totally-real-number-fields-lenny-fukshansky-cmc/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20221129T122500
DTEND;TZID=America/Los_Angeles:20221129T131500
DTSTAMP:20260501T100143
CREATED:20221110T030247Z
LAST-MODIFIED:20221124T032038Z
UID:2989-1669724700-1669727700@colleges.claremont.edu
SUMMARY:Partial orders on standard Young tableaux( Gizem Karaali\, Pomona)
DESCRIPTION:Young diagrams are all possible arrangements of n boxes into rows and columns\, with the number of boxes in each subsequent row weakly decreasing. For a partition λ of n\, a standard Young tableau S of shape λ is built from the Young diagram of shape λ by filling it with the numbers 1 to n\, each occurring exactly once in such a way that the numbers are strictly increasing across rows (left to right) and down columns. Young diagrams with n cells are in one-to-one correspondence with the irreducible representations of the symmetric group Sn\,; the standard Young tableaux count the dimensions of these irreps and thus are some of the most essential objects of combinatorial representation theory and algebraic combinatorics. In this talk\, based on joint work with Isabella Senturia (PO’20) and Müge Taskin\, I will describe a handful of partial orders already defined on SYTn\, the set of all standard Young tableaux with n cells\, and propose a new one.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-gizem-karaali-pomona-2/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20221115T121500
DTEND;TZID=America/Los_Angeles:20221115T131000
DTSTAMP:20260501T100143
CREATED:20220823T003904Z
LAST-MODIFIED:20221102T220943Z
UID:2786-1668514500-1668517800@colleges.claremont.edu
SUMMARY:Minimal Mahler measure in number fields (Kate Petersen\, University of Minnesota Duluth)
DESCRIPTION:The Mahler measure of a polynomial is the modulus of its leading term multiplied by the moduli of all roots outside the unit circle.  The Mahler measure of an algebraic number b\, M(b) is the Mahler measure of its minimal polynomial. By a result of Kronecker\, an algebraic number b satisfies M(b)=1 if and only if b is a root of unity. Famously\, Lehmer asked if there are algebraic numbers with Mahler measures arbitrarily close to 1 (but not equal to 1). We will investigate the minimal Mahler measure of a number field.  For a number field K this is the smallest Mahler measure of a non-torsion generator for K\, written M(K). There are known upper and lower bounds for M(K) in terms of the degree and discriminant of K.  Focusing on cubics\, we will discuss how these bounds correspond to other properties of the number field\, and the sharpness of these bounds.  This is joint work with Lydia Eldredge.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-kate-petersen-university-of-minnesota-duluth/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20221108T121500
DTEND;TZID=America/Los_Angeles:20221108T131000
DTSTAMP:20260501T100143
CREATED:20220824T204820Z
LAST-MODIFIED:20221031T203245Z
UID:2787-1667909700-1667913000@colleges.claremont.edu
SUMMARY:Factoring translates of polynomials (Arvind Suresh\, University of Arizona - Tucson)
DESCRIPTION:Given a degree d polynomial f(x) in Q[x]\, consider the subset S_f  of Q consisting of rational numbers t for which the translated polynomial f(x) – t factors completely in Q[x]. For example\, if f is linear or quadratic then S_f is always infinite\, but if degree of f is at least 3\, then interesting things can happen. In this talk\, we discuss a connection between the set S_f and the classical Prouhet–Tarry–Escott problem (which asks for integer solutions to certain symmetric family of equations)\, and we present two infinite families of polynomials f for which S_f is infinite (upon replacing Q with certain number fields). Time permitting\, we outline how these can then be used to produce algebraic curves over number fields having a record number of rational points (relative to their genus).
URL:https://colleges.claremont.edu/ccms/event/antc-talk-arvind-suresh-university-of-arizona-tucson/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20221101T121500
DTEND;TZID=America/Los_Angeles:20221101T131000
DTSTAMP:20260501T100143
CREATED:20220906T211012Z
LAST-MODIFIED:20221031T180722Z
UID:2839-1667304900-1667308200@colleges.claremont.edu
SUMMARY:A tale of two worlds: parking functions &  reduction algebras (Dwight Anderson Williams II\, Pomona)
DESCRIPTION:“A Tale of Two Cities” is a novel told in three books/parts. Here we describe three projects related both to published work and ongoing pieces: \nPROJECT 1: In the world of combinatorics\, parking functions are combinatorial objects arising from the situation of parking cars under a parking strategy. In this part of the talk\, we will refresh the notion of classical parking functions given by the classical parking rules/strategy. We will then state an interesting correspondence between certain classical parking functions and so-called ideal states of the famous Tower of Hanoi game. This work is to appear in The American Mathematical Monthly with the following co-authors: Y. Aguillon\, D. Alvarenga\, P.E. Harris\, S. Kotapati\, J.C. Martinez Mori\, C. Monroe\, Z. Saylor\, and C. Tieu. \nPROJECT 2: In the world of algebra\, we shed light on representation theory of Lie superalgebras by constructing reduction algebras. These algebras provide structures to study in their own right\, and we give an example in presenting the diagonal reduction algebra of $osp(1|2)$\, first described in a joint paper with Jonas T. Hartwig. \nPROJECT 3: Continuing down an algebraic pathway\, we summarize the general framework given by Zhelobenko to apply representation theory of reduction algebras as a method to solve equations. Fixing equations important to the study of physics has led to recent work with Jonas T. Hartwig and Erin Dolecheck\, as well\, Irmak Bukey.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-dwight-anderson-williams-ii-pomona/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20221025T121500
DTEND;TZID=America/Los_Angeles:20221025T131000
DTSTAMP:20260501T100143
CREATED:20220906T160323Z
LAST-MODIFIED:20221012T181637Z
UID:2834-1666700100-1666703400@colleges.claremont.edu
SUMMARY:Properties of redistricting Markov chains (Sarah Cannon\, CMC)
DESCRIPTION:Markov chains have become widely-used to generate random political districting plans. These random districting plans can be used to form a baseline for comparison\, and any proposed districting plans that differ significantly from this baseline can be flagged as potentially gerrymandered. However\, very little is rigorously known about these Markov chains – Are they irreducible? What is their mixing time? For some\, even the stationary distribution remains unknown. I will present recent work that answers some of these questions\, which uses tools from probability\, computational geometry\, and more.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-sarah-cannon-cmc/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20221011T121500
DTEND;TZID=America/Los_Angeles:20221011T131000
DTSTAMP:20260501T100143
CREATED:20220825T192011Z
LAST-MODIFIED:20221004T211454Z
UID:2794-1665490500-1665493800@colleges.claremont.edu
SUMMARY:On the geometry of lattice extensions (Max Forst\, CGU)
DESCRIPTION:Given a lattice L\, an extension of L is a lattice M of strictly greater rank so that L is equal to the intersection of the subspace spanned by L with M. In this talk\, we will discus constructions of such lattice extensions with particular geometric invariants of M\, such as the determinant\, covering radius and successive minima related to the analogous invariants of L. Joint work with Lenny Fukshansky.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-max-forst-cgu/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20221004T121500
DTEND;TZID=America/Los_Angeles:20221004T131000
DTSTAMP:20260501T100143
CREATED:20220829T210323Z
LAST-MODIFIED:20221003T234340Z
UID:2800-1664885700-1664889000@colleges.claremont.edu
SUMMARY:Recent developments on the slice rank polynomial method with applications (Mohamed Omar\, HMC)
DESCRIPTION:The slice rank polynomial method\, motivated by groundbreaking work of Croot\, Lev and Pach and refined by Tao\, has opened the door to the resolution of many problems in extremal combinatorics. We survey these results and discuss contributions in several of the speaker’s recent papers.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-mohamed-omar-hmc/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220927T121500
DTEND;TZID=America/Los_Angeles:20220927T131000
DTSTAMP:20260501T100143
CREATED:20220906T160640Z
LAST-MODIFIED:20220922T053209Z
UID:2836-1664280900-1664284200@colleges.claremont.edu
SUMMARY:Spinning switches on a wreath product (Peter Kagey\, HMC)
DESCRIPTION:This talk discusses a puzzle called “Spinning Switches\,” based on a problem popularized by Martin Gardner in his February 1979 column of “Mathematical Games”. This puzzle can be generalized to a two-player game on a finite wreath products. This talk will provide a classification of several families of these generalized puzzles\, including a full classification in the case of Abelian groups.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-peter-kagey-hmc/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220920T121500
DTEND;TZID=America/Los_Angeles:20220920T131000
DTSTAMP:20260501T100143
CREATED:20220811T002022Z
LAST-MODIFIED:20220906T231455Z
UID:2780-1663676100-1663679400@colleges.claremont.edu
SUMMARY:Arithmetical structures (Luis Garcia Puente\, Colorado College)
DESCRIPTION:An arithmetical structure on a finite\, connected graph G without loops is given by an assignment of positive integers to the vertices such that\, at each vertex\, the integer there is a divisor of the sum of the integers at adjacent vertices\, counted with multiplicity if the graph is not simple. Alternatively\,  an arithmetical structure on G is a pair  of positive integer vectors (d\,r) such that  Mr = 0\, where M = diag(d) – A  is a square matrix whose diagonal entries are given by the vector d\, and whose off-diagonal elements are given by the negative adjacency matrix of G. Arithmetical structures were first introduced by Lorenzini in 1989; matrices of the form (diag(d) – A) arise in algebraic geometry as intersection matrices of degenerating curves.  However\, they also naturally appear in the context of algebraic graph theory as matrices of the form  (diag(d) – A)  generalize the Laplacian matrix of a graph.\n\nIn this talk\, I will give an introduction to the topic. We will discuss some combinatorial\, structural and computational aspects of arithmetical structures. In particular\, we will count the number of distinct arithmetical structures on certain graph families such as path\, cycle\, complete and bident graphs. For paths\, we will show that arithmetical structures are enumerated by the Catalan numbers. For cycles\, we prove that arithmetical structures are enumerated by the binomial coefficients C(2n-1\,n-1).  We will also discuss results about the associated critical group of an arithmetical structure\, i.e.\,  the cokernel of the matrix M.   This talk will be accessible to undergraduate students with some knowledge of linear algebra and discrete mathematics.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-luis-garcia-puente-colorado-college/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220913T121500
DTEND;TZID=America/Los_Angeles:20220913T131000
DTSTAMP:20260501T100143
CREATED:20220902T001706Z
LAST-MODIFIED:20220906T231347Z
UID:2814-1663071300-1663074600@colleges.claremont.edu
SUMMARY:Kriz's theorem via dynamics of linear operators (Yunied Puig de Dios\, CMC)
DESCRIPTION:The existence of a set $A\subset \N_0$ of positive upper Banach density such that $A-A:=\{m-n:m\, n\in A\, m>n\}$ does not contain a set of the form $S-S$ with $S$ a piecewise syndetic is in essence the content of a popular result due to K\v r\'{i}\v z in 1987. Since then at least four different proofs of this result have been given\, and all of them give basically the example originally exhibited by K\v r\'{i}\v z when viewed appropriately. We obtain a generalization of K\v r\'{i}\v z’s result. Our approach differs completely from the previous ones\, as this would be the first proof of K\v r\'{i}\v z’s Theorem which does not rely on Lov\'{a}sz’s Theorem for chromatic numbers of Kneser graphs. Furthermore\, it is done via operator theory\, namely using dynamics of bounded linear operators on infinite-dimensional complex separable Banach spaces. As a consequence\, our example is genuinely different from the one exhibited  originally by K\v r\'{i}\v z.
URL:https://colleges.claremont.edu/ccms/event/krizs-theorem-via-dynamics-of-linear-operators-yunied-puig-de-dios-cmc/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220906T121500
DTEND;TZID=America/Los_Angeles:20220906T131000
DTSTAMP:20260501T100143
CREATED:20220811T001752Z
LAST-MODIFIED:20220902T173415Z
UID:2779-1662466500-1662469800@colleges.claremont.edu
SUMMARY:Monodromy groups of Belyi Lattes maps (Edray Goins\, Pomona College)
DESCRIPTION:An elliptic curve $ E: y^2 + a_1 \\, x \\, y + a_3 \\, y = x^3 + a_2 \\, x^2 + a_1 \\, x + a_6 $ is a cubic equation which has two curious properties: (1) the curve is nonsingular\, so that we can draw tangent lines to every point $ P = (x\,y) $ on the curve; and (2) the collection of complex points\, namely $ E(\mathbb C) $\, forms an abelian group under a certain binary operation $ \bigoplus: E(\mathbb C) \times E(\mathbb C) \to E(\mathbb C) $.   In particular\, for every positive integer $N$\, the map $ P \mapsto [N] P $ which adds a point $ P \in E(\mathbb C) $ to itself $N$ times is a group homomorphism.   A rational map $\gamma: \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C) $ from the Riemann Sphere to itself is said to be a Latt\`{e}s Map if there are “well-behaved” maps $ \phi: E(\mathbb C) \to \mathbb P^1(\mathbb C) $ and $\psi: E(\mathbb C) \to E(\mathbb C) $ such that $\gamma \circ \phi = \phi \circ \psi$.  We are interested in those Latt\`{e}s Maps $\gamma$ which are also Bely\u{\i} Maps\, that is\, the only critical values are $ 0 $\, $ 1 $\, and $ \infty $.  Work of Zeytin classifies all such maps: For example\, if $ E: y^2 = x^3 + 1 $ then $ \phi: (x\,y) \mapsto (y+1)/2 $ while $\psi = [N] $ for some positive integer $N$.\n\nWe would like to know more about Bely\u{\i} Latt\`{e}s Maps $\gamma$.  What can we say about such maps?  What are their Dessin d’Enfants?  In some cases\, this is a bipartite graph with $ 3 \\, N^2 $ vertices.  What are their monodromy groups? Sometimes this is a group of size $ 3 \\, N^2 $.  In this talk\, we explain the complete answers to these questions\, exploiting the relationship between fundamental groups of Riemann surfaces and Galois groups of function fields.  This work is conducted as part of the Pomona Research in Mathematics Experience (DMS-2113782).
URL:https://colleges.claremont.edu/ccms/event/monodromy-groups-of-belyi-lattes-maps-edray-goins-pomona-college/
LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220503T123000
DTEND;TZID=America/Los_Angeles:20220503T132000
DTSTAMP:20260501T100143
CREATED:20220128T185315Z
LAST-MODIFIED:20220418T040129Z
UID:2583-1651581000-1651584000@colleges.claremont.edu
SUMMARY:Beran’s tests of uniformity for discrete data (Michael Orrison\, HMC)
DESCRIPTION:Suppose you are given a data set that can be viewed as a nonnegative integer-valued function defined on a finite set. A natural question to ask is whether the data can be viewed as a sample from the uniform distribution on the set\, in which case you might want to apply some sort of test of uniformity to the data. In this talk\, I will share some work Anna Bargagliotti (Loyola Marymount University) and I have been doing to better understand a particular class of tests of uniformity first described in a 1968 paper written by R.J. Beran. Our approach uses tools from harmonic analysis on finite groups\, and in this talk I will introduce those tools and then show how they can easily be used when working with discrete circular data.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-michael-orrison-hmc/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
END:VCALENDAR