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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240326T121500
DTEND;TZID=America/Los_Angeles:20240326T131000
DTSTAMP:20260430T143257
CREATED:20231215T050545Z
LAST-MODIFIED:20240312T172417Z
UID:3331-1711455300-1711458600@colleges.claremont.edu
SUMMARY:Sublattices and subrings of Z^n and random finite abelian groups (Nathan Kaplan\, UC Irvine)
DESCRIPTION:How many sublattices of Zn have index at most X?  If we choose such a lattice L at random\, what is the probability that Zn/L is cyclic?  What is the probability that its order is odd?  Now let R be a random subring of Zn.  What is the probability that Zn/R is cyclic?  We will see how these questions fit into the study of random groups in number theory and combinatorics.  We will discuss connections to Cohen-Lenstra heuristics for class groups of number fields\, sandpile groups of random graphs\, and cokernels of random matrices over the integers.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-nathan-kaplan-uc-irvine/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240319T121500
DTEND;TZID=America/Los_Angeles:20240319T131000
DTSTAMP:20260430T143257
CREATED:20231025T032921Z
LAST-MODIFIED:20240206T000905Z
UID:3302-1710850500-1710853800@colleges.claremont.edu
SUMMARY:Almost-prime times in horospherical flows (Taylor McAdam\, Pomona)
DESCRIPTION:There is a rich connection between homogeneous dynamics and number theory.  Often in such applications it is desirable for dynamical results to be effective (i.e. the rates of convergence for dynamical phenomena are known).  In the first part of this talk\, I will provide the necessary background and relevant history to state an effective equidistribution result for horospherical flows on the space of unimodular lattices in R^n.  I will then describe an application to studying the distribution of almost-prime times (integer times having fewer than a fixed number of prime factors) in horospherical orbits and discuss connections of this work to Sarnak’s Mobius disjointness conjecture.  In the second part of the talk I will describe some of the ingredients and key steps that go into proving these results. If time allows\, I will conclude by discussing recent results and ongoing work with M. Luethi that strengthens and generalizes this work.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-taylor-mcadam-pomona/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240305T121500
DTEND;TZID=America/Los_Angeles:20240305T131000
DTSTAMP:20260430T143257
CREATED:20240206T040319Z
LAST-MODIFIED:20240206T040319Z
UID:3376-1709640900-1709644200@colleges.claremont.edu
SUMMARY:Homological mirror symmetry\, curve counting\, and a classical example: 27 lines on a nonsingular cubic surface (Reggie Anderson\, CMC)
DESCRIPTION:Though mirror symmetry requires much technical background\, it gained traction in the mathematical community when physicists Candelas-de la Ossa-Green-Parkes discovered enumerative invariants counting the number of rational degree d curves inside of certain space called a “quintic threefold.” This answered longstanding problems in enumerative geometry from antiquity. In particular\, the number of rational degree d=1 curves inside of the space counts the number of lines. We will review a simpler\, classical example: any nonsingular cubic surface contains exactly 27 lines.
URL:https://colleges.claremont.edu/ccms/event/homological-mirror-symmetry-curve-counting-and-a-classical-example-27-lines-on-a-nonsingular-cubic-surface-reggie-anderson-cmc/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240227T121500
DTEND;TZID=America/Los_Angeles:20240227T131000
DTSTAMP:20260430T143257
CREATED:20240126T230120Z
LAST-MODIFIED:20240221T014138Z
UID:3354-1709036100-1709039400@colleges.claremont.edu
SUMMARY:The restricted variable Kakeya problem (Pete Clark\, University of Georgia)
DESCRIPTION:For a finite field F_q\, a subset of F_q^N is a Kakeya set if it contains a line in every direction (i.e.\, a coset of every one-dimensional linear subspace).  The finite field Kakeya problem is to determine the minimal size K(N\,q) of a Kakeya set in F_q^N.  This problem was posed by Wolff in 1999 as an analogue to the Kakeya problem in Euclidean N-space\, which was (and still is) one of the major open problems in harmonic analysis.  It caused quite a stir in 2008 when Zeev Dvir showed that for each fixed N\, as q -> oo\, K(N\,q) is bounded below by a constant times q^N: the Euclidean analogue of this result is not only proved but known to be false.\n\nBut what about the constant?  In 2009 Dvir-Kopparty-Saraf-Sudan gave a lower bound on K(N\,q) that was within a factor of 2 of an upper bound due to Dvir-Thas.  (I will briefly mention recent work of Bukh-Chao giving a decisive further improvement\, but that is not the focus of the talk.) The key to this improved lower bound is a multiplicity enhancement of a 1922 result of Ore. In this talk I want to give my own exposition of this work together with a mild generalization: if X is a subset of F_q^N \ {0}\, then an X-Kakeya set is a subset that contains a translate of the line generated by x for all x in X.  Putting K_X(N\,q) to be the minimal size of an X-Kakeya set in F_q^N\, I will give a lower bound on K_X(N\,q) that recovers the DKSS bound when X = F_q^N \ {0}.  This is similar in spirit to  “statistical Kakeya” results of Dvir and DKSS but not overlapping much; in fact\, I will give a statistical generalization of my result as well.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-pete-clark-university-of-georgia/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240220T121500
DTEND;TZID=America/Los_Angeles:20240220T131000
DTSTAMP:20260430T143257
CREATED:20231127T045722Z
LAST-MODIFIED:20240219T164238Z
UID:3328-1708431300-1708434600@colleges.claremont.edu
SUMMARY:Point-counting and topology of algebraic varieties (Siddarth Kannan\, UCLA)
DESCRIPTION:A projective algebraic variety X is the zero locus of a collection of homogeneous polynomials\, in projective space. When the polynomials have integer coefficients\, we can think of the k-valued points X(k) of the variety\, for any field k. Now suppose we have two different fields k and k’. How does the behavior of X(k) inform the behavior of X(k’)? It turns out that this is a rich line of inquiry. I will present a particularly pleasing example which relates the topology of the complex-valued points of X with the number of points it has over finite fields.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-siddarth-kannan-ucla/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240213T121500
DTEND;TZID=America/Los_Angeles:20240213T131000
DTSTAMP:20260430T143257
CREATED:20240116T192503Z
LAST-MODIFIED:20240116T202510Z
UID:3335-1707826500-1707829800@colleges.claremont.edu
SUMMARY:Quiver categorification of quandle invariants (Sam Nelson\, CMC)
DESCRIPTION:Quiver structures are naturally associated to subsets of the endomorphism sets of quandles and other knot-coloring structures\, providing a natural form of categorification of homset invariants and their enhancements. In this talk we will survey recent work in this area.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-sam-nelson-cmc-3/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240123T121500
DTEND;TZID=America/Los_Angeles:20240123T131000
DTSTAMP:20260430T143257
CREATED:20231020T203433Z
LAST-MODIFIED:20240117T005624Z
UID:3294-1706012100-1706015400@colleges.claremont.edu
SUMMARY:Using quantum statistical mechanical systems to study real quadratic fields (Jane Panangaden\, Pitzer College)
DESCRIPTION:The original Bost-Connes system was constructed in 1990 and is a QSM system with deep connections to the field of rationals. In particular\, its partition function is the Riemann-zeta function and its ground states evaluated on certain arithmetic objects yield generators of the maximal Abelian extension of the rationals. In this talk we describe the construction of a related QSM system adapted to the study of real quadratic fields\, called the Boundary GL2 System. We describe its thermal properties and show how these relate to class field theory of real quadratic fields. These results are joint work with Matilde Marcolli.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-jane-panangaden-pitzer-college/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20231205T121500
DTEND;TZID=America/Los_Angeles:20231205T131000
DTSTAMP:20260430T143257
CREATED:20230926T180257Z
LAST-MODIFIED:20231130T000041Z
UID:3260-1701778500-1701781800@colleges.claremont.edu
SUMMARY:Skein algebra of a punctured surface (Helen Wong\, CMC)
DESCRIPTION:The Kauffman bracket skein algebra of a surface is at once related to quantum topology and to hyperbolic geometry. In this talk\, we consider a generalization of the skein algebra due to Roger and Yang for surfaces with punctures. In joint work with Han-Bom Moon\, we show that the generalized skein algebra is a quantization of Penner’s decorated Teichmuller space\, which consists of complete metrics of the surface with extra decoration at the punctures. Interestingly\, our proof relies on a connection between the skein algebra and the cluster algebras of tagged arcs due to Fomin\, Shapiro\, and Thurston.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-helen-wong-cmc-2/
LOCATION:Roberts North 102\, CMC
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20231128T121500
DTEND;TZID=America/Los_Angeles:20231128T131000
DTSTAMP:20260430T143257
CREATED:20231009T153250Z
LAST-MODIFIED:20231121T192204Z
UID:3281-1701173700-1701177000@colleges.claremont.edu
SUMMARY:What can chicken nuggets tell us about symmetric functions\, positive polynomials\, random norms\, and AF algebras? (Stephan Garcia\, Pomona)
DESCRIPTION:A simple question about chicken nuggets connects everything from analysis and combinatorics to probability theory and computer-aided design.  With tools from complex\, harmonic\, and functional analysis\, probability theory\, algebraic combinatorics\, and spline theory\, we answer many asymptotic questions about factorization lengths in numerical semigroups.  Our results yield uncannily accurate predictions\, along with unexpected results about symmetric functions\, trace polynomials\, and the statistical properties of certain AF C$^*$-algebras.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-stephan-garcia-pomona/
LOCATION:Roberts North 102\, CMC
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20231121T121500
DTEND;TZID=America/Los_Angeles:20231121T131000
DTSTAMP:20260430T143257
CREATED:20231009T193529Z
LAST-MODIFIED:20231119T201433Z
UID:3282-1700568900-1700572200@colleges.claremont.edu
SUMMARY:On the Cox ring of a weighted projective plane blown-up at a point (Javier Gonzalez Anaya\, HMC)
DESCRIPTION:The Cox ring of a projective variety is the ring of all its meromorphic functions\, together with a grading of geometric origin. Determining whether this ring is finitely generated is a challenging task\, even for simple examples. In this talk\, we will discuss our efforts to tackle this problem for a specific class of varieties\, known as blow-ups of weighted projective planes (WPP). Through the lens of toric geometry\, a WPP is characterized by a rational plane triangle. This allows us to reinterpret the problem combinatorially and show that the solution often emerges from a parameter space of such triangles. This is joint work with José Luis González and Kalle Karu.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-javier-gonzalez-anaya-hmc/
LOCATION:Roberts North 102\, CMC
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20231114T121500
DTEND;TZID=America/Los_Angeles:20231114T131000
DTSTAMP:20260430T143257
CREATED:20230908T055625Z
LAST-MODIFIED:20231109T070158Z
UID:3177-1699964100-1699967400@colleges.claremont.edu
SUMMARY:f^*-vectors of lattice polytopes (Max Hlavacek\, Pomona College)
DESCRIPTION:The Ehrhart polynomial of a lattice polytope P counts the number of integer points in the nth integral dilate of P. The f^* -vector of P\, introduced by Felix Breuer in 2012\, is the vector of coefficients of the Ehrhart polynomial with respect to the binomial coefficient basis . Similarly to h and h^* -vectors\, the f^* -vector of P coincides with the f-vector (counting faces of every dimension) of its unimodular triangulations (if they exist). We give several inequalities that hold among the coefficients of f^*-vectors of polytopes. These inequalities resemble striking similarities with existing inequalities for the coefficients of f-vectors of simplicial polytopes. Even though f^* -vectors of polytopes are not always unimodal\, we describe several families of polytopes that carry the unimodality property.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-max-hlavacek-pomona-college/
LOCATION:Roberts North 102\, CMC
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20231107T121500
DTEND;TZID=America/Los_Angeles:20231107T131000
DTSTAMP:20260430T143257
CREATED:20230908T055420Z
LAST-MODIFIED:20231024T041512Z
UID:3176-1699359300-1699362600@colleges.claremont.edu
SUMMARY:Frobenius coin-exchange generating functions (Matthias Beck\, San Francisco State University)
DESCRIPTION:We study variants of the Frobenius coin-exchange problem: Given n positive relatively prime parameters\, what is the largest integer that cannot be represented as a nonnegative integral linear combination of the given integers? This problem and its siblings can be understood through generating functions with 0/1 coefficients according to whether or not an integer is representable. In the 2-parameter case\, this generating function has an elegant closed form\, from which many corollaries follow\, including a formula for the Frobenius problem. We establish a similar closed form for the generating function indicating all integers with exactly k representations\, with similar wide-ranging corollaries. This is joint work with Leonardo Bardomero.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-matthias-beck-san-francisco-state-university/
LOCATION:Roberts North 102\, CMC
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20231031T121500
DTEND;TZID=America/Los_Angeles:20231031T131000
DTSTAMP:20260430T143257
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:20260430T143257
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:20260430T143257
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:20260430T143257
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:20260430T143257
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:20260430T143257
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:20260430T143257
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:20260430T143257
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:20260430T143257
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:20260430T143257
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:20260430T143257
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:20260430T143257
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:20260430T143257
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:20260430T143257
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:20260430T143257
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:20260430T143257
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:20260430T143257
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:20260430T143257
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
END:VCALENDAR