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DTSTART;TZID=America/Los_Angeles:20260505T121500
DTEND;TZID=America/Los_Angeles:20260505T131000
DTSTAMP:20260622T142532
CREATED:20260119T224840Z
LAST-MODIFIED:20260427T163251Z
UID:3962-1777983300-1777986600@colleges.claremont.edu
SUMMARY:Voting on relations using pairs information (Michael Orrison\, HMC)
DESCRIPTION:Many aggregation problems ask us to turn individual judgments into a single collective outcome. In this talk\, we model each voter’s input as a relation on a set of alternatives\, allowing pairwise comparisons to include strict preferences\, ties\, or incomparability. This perspective gives a common framework for median procedures and scoring methods\, including several familiar voting rules. The distance-based side leads naturally to graphs such as the hypercube of relations\, while the scoring-based side leads to questions about linear operators on functions on relations. At the center is a natural four-parameter family of scoring matrices whose eigenspace decompositions separate meaningful types of pairwise information\, connecting voting theory with graph theory\, linear algebra\, and harmonic analysis. \nThis is joint work with Karl-Dieter Crisman\, Erin McNicholas\, and Kathryn Nyman.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-michael-orrison-hmc/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20260428T121500
DTEND;TZID=America/Los_Angeles:20260428T131000
DTSTAMP:20260622T142532
CREATED:20260123T011543Z
LAST-MODIFIED:20260422T205356Z
UID:3970-1777378500-1777381800@colleges.claremont.edu
SUMMARY:Coordinate ring of the universal centralizer via Demazure operators (Tom Gannon\, UCR)
DESCRIPTION:One of the key objects used in Ngo’s proof of the fundamental lemma is the group scheme of universal centralizers associated to a split reductive group G. In this talk\, we’ll discuss forthcoming work\, joint with Victor Ginzburg\, which describes the coordinate ring of the group scheme of universal centralizers in terms of the root datum of G using Demazure (or divided difference) operators. We will then discuss how our result follows from a more general computation on Weil restriction and\, time permitting\, we will discuss a potential generalization of our result to Coulomb branches.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-tom-gannon-ucr/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20260421T121500
DTEND;TZID=America/Los_Angeles:20260421T131000
DTSTAMP:20260622T142532
CREATED:20260123T053557Z
LAST-MODIFIED:20260415T053435Z
UID:3972-1776773700-1776777000@colleges.claremont.edu
SUMMARY:Diophantine avoidance\, primitive elements\, and normal basis theorem (Sehun Jeong\, CMC)
DESCRIPTION:Diophantine avoidance has been studied by several authors in recent years. This refers to effective results on existence of points of bounded size in a given algebraic set avoiding some specified subsets. The famous primitive element theorem states that every number field K is of the form Q(a) for some element a in K. From the proof of this theorem\, it is clear that not only there are infinitely many such primitive elements in K\, but in fact most elements in K are primitive. One natural question to ask is about finding a primitive element of small “size”\, where we use a height function to measure size. We discuss the conjecture of Ruppert and known results in this direction\, as well as our recent work on this problem. In addition\, we provide the standard and effective version of normal basis theorem\, obtaining an explicit bound in terms of the degree and discriminant of K\, where K/Q is a Galois extension. At the end\, we discuss a particularly good bound in the case of prime degree. This is joint work with Lenny Fukshansky.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-sehun-jeong-cmc/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20260414T121500
DTEND;TZID=America/Los_Angeles:20260414T131000
DTSTAMP:20260622T142532
CREATED:20260123T051413Z
LAST-MODIFIED:20260407T032128Z
UID:3971-1776168900-1776172200@colleges.claremont.edu
SUMMARY:Knot complements\, series invariants and Lie superalgebra (John Yoonseok Chae)
DESCRIPTION:Inspired by the categorification program for a numerical invariant of three-manifolds\, series invariants for closed manifolds and for knot complements were introduced. This in turn motivated an extension of the series invariant of the former case to Lie superalgebras. It was recently generalized to knot complements. In this talk\, we review the original series invariants and introduce the recent generalization and explore its properties and examples.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-helen-wong-cmc/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20260407T121500
DTEND;TZID=America/Los_Angeles:20260407T131000
DTSTAMP:20260622T142532
CREATED:20260120T211724Z
LAST-MODIFIED:20260331T041748Z
UID:3963-1775564100-1775567400@colleges.claremont.edu
SUMMARY:Tropical linear series and matroids (Dagan Karp\, HMC)
DESCRIPTION:In this talk\, I’ll attempt to give a friendly introduction to tropical linear series and explore their relationship to matroid theory. Along the way\, we’ll stop to admire the beautiful view from enumerative geometry and combinatorics. This is joint work with Chih-Wei Chang\, Matthew Dupraz\, Hernan Iriarte\, David Jensen\, Sam Payne\, and Jidong Wang\, and also with Jenna Luo. 
URL:https://colleges.claremont.edu/ccms/event/antc-talk-dagan-karp-hmc-2/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20260331T121500
DTEND;TZID=America/Los_Angeles:20260331T131000
DTSTAMP:20260622T142532
CREATED:20260106T162953Z
LAST-MODIFIED:20260321T145212Z
UID:3941-1774959300-1774962600@colleges.claremont.edu
SUMMARY:Central moments of autocorrelation demerit factors of binary sequences (Daniel Katz\, CSUN)
DESCRIPTION:A low autocorrelation binary sequence of length $\ell$ is an $\ell$-tuple of $+1$s and $-1$s that does not strongly resemble any translate of itself.  Such sequences are used in communications and remote sensing for synchronization and ranging\, where translation represents time delay.  A single number that indicates how good a sequence is for such purposes\, called the merit factor\, was introduced by Golay.  Its reciprocal is the demerit factor\, which is more natural to analyze due to its connection with norms of polynomials on the complex unit circle.  We consider the uniform probability measure on the $2^\ell$ binary sequences of length $\ell$ and investigate the distribution of the demerit factors of these sequences.  Sarwate and Jedwab have respectively calculated the mean and variance of this distribution. For each positive integer $p$\, we derive a formula for the $p$th central moment of the demerit factor for the binary sequences of length $\ell$; this is $\ell^{-2 p}$ times a quasipolynomial function of $\ell$.  The derivations rely on new combinatorial techniques\, assisted by group theory and Ehrhart theory\, and show that all the central moments are strictly positive for $p\geq 2$ and $\ell \geq 4$. Jedwab’s formula for variance is confirmed\, and we go beyond previous results by also deriving an exact formula for the skewness (by hand) and for the kurtosis and the fifth moment (by computer).  We obtain asymptotic values for all central moments in the limit as the length $\ell$ of the sequences tends to infinity.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-daniel-katz-csun/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20260324T121500
DTEND;TZID=America/Los_Angeles:20260324T131000
DTSTAMP:20260622T142532
CREATED:20260209T235439Z
LAST-MODIFIED:20260226T211019Z
UID:3991-1774354500-1774357800@colleges.claremont.edu
SUMMARY:Computing certificates for complete positivity (Achill Schürmann\, University of Rostock)
DESCRIPTION:A key problem in computer proofs based on solutions from copositive optimization\, is checking whether or not a given quadratic form is completely positive or not. In this talk we describe the first known algorithm for arbitrary rational input. It is based on a suitable adaption of Voronoi’s Algorithm and the underlying theory from positive definite to copositive quadratic forms. We observe several similarities with the classical theory\, but also some differences\, in particular for three and more variables. A key element and currently the main bottleneck in our algorithm is an adapted shortest vector computation\, asking for all nonnegative integer vectors attaining the copositive minimum of a given copositive quadratic form. \n(based on joint work with Valentin Dannenberg\, Alexander Oertel\, Mathieu Dutour Sikiric and Frank Vallentin)
URL:https://colleges.claremont.edu/ccms/event/antc-talk-achill-schurmann-university-of-rostock/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20260310T123000
DTEND;TZID=America/Los_Angeles:20260310T131000
DTSTAMP:20260622T142532
CREATED:20260119T182717Z
LAST-MODIFIED:20260307T023545Z
UID:3961-1773145800-1773148200@colleges.claremont.edu
SUMMARY:Hecke algebras and motives (Robert Cass\, CMC)
DESCRIPTION:Hecke algebras play a central role in both number theory and representation theory. While some Hecke algebras have explicit descriptions in terms of generators and relations\, others are understood through structure constants that encode multiplicities in tensor products of representations. In this talk\, I will discuss several projects with Thibaud van den Hove and Jakob Scholbach aimed at using geometry and motives to give a uniform categorification of Hecke algebras. Along the way\, we will encounter the geometric Satake equivalence\, Gaitsgory’s central functor\, and Iwahori-Whittaker models.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-robert-cass-cmc-2/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20260303T121500
DTEND;TZID=America/Los_Angeles:20260303T131000
DTSTAMP:20260622T142532
CREATED:20260302T023221Z
LAST-MODIFIED:20260302T023221Z
UID:4013-1772540100-1772543400@colleges.claremont.edu
SUMMARY:On a new version of Siegel’s lemma  (Lenny Fukshansky\, CMC)
DESCRIPTION:The classical Siegel’s lemma (1929) asserts the existence of a nontrivial integer solution to an underdetermined integer homogeneous linear system\, whose “size” is small as compared to the size of the coefficients of the system. Far-reaching generalizations of this theorem\, producing a full basis for the solution space\, were obtained over number fields by Bombieri & Vaaler (1983)\, and over the field of algebraic numbers by Roy & Thunder (1996)\, where the “size” was measured by a height function. We obtain a new version of Siegel’s lemma\, bridging the Bombieri & Vaaler and Roy & Thunder results in two ways: (1) our basis lies over a fixed number field as in Bombieri & Vaaler’s theorem; (2) our height-bound does not depend on the number field in question as in Roy & Thunder’s theorem. Our result does not imply the previously established ones and is not implied by them\, and our basis has some additional interesting properties. Our method is quite different from the previous ones\, using only linear algebra. Joint work with Max Forst.
URL:https://colleges.claremont.edu/ccms/event/on-a-new-version-of-siegels-lemma-lenny-fukshansky-cmc/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20260217T121500
DTEND;TZID=America/Los_Angeles:20260217T131000
DTSTAMP:20260622T142532
CREATED:20260121T181315Z
LAST-MODIFIED:20260211T173037Z
UID:3964-1771330500-1771333800@colleges.claremont.edu
SUMMARY:Summer of Math Discovery: Two research projects on combinatorial polytopes (Andrés R. Vindas Meléndez\, HMC)
DESCRIPTION:This is a talk in two parts covering two projects that the speaker mentored over the summer of 2025. The first project deals with the study of polytopes that arise from the convex hulls of stack-sorting on particular permutations. The second project deals with the study of symmetric edge polytopes of a finite simple graph\, a centrally symmetric lattice polytope whose vertices are defined by the edges of the graph. Both projects studied the (Euclidean\, relative\, or normalized) volumes of the respective combinatorially defined polytope.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-andres-r-vindas-melendez-hmc/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20260203T121500
DTEND;TZID=America/Los_Angeles:20260203T131000
DTSTAMP:20260622T142532
CREATED:20260129T172206Z
LAST-MODIFIED:20260129T215939Z
UID:3977-1770120900-1770124200@colleges.claremont.edu
SUMMARY:Relationships between skein algebras (Helen Wong\, CMC)
DESCRIPTION:We will examine the multiplicative structure of two skein algebras— the usual Kauffman bracket skein algebra of a surface (generated by loops) and a generalization of it due to Roger-Yang (generated by loops and arcs).   In joint work with Chloe Marple\, we found a homomorphism between the usual skein algebra for a closed torus and the Roger-Yang skein algebra for a twice-punctured annulus.   In this talk\, I’ll present some ways we used that homomorphism to do computations\, and whether there might be similar relationships between skein algebras of other surfaces. 
URL:https://colleges.claremont.edu/ccms/event/antc-talk-helen-wong-cmc-2/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20260127T121500
DTEND;TZID=America/Los_Angeles:20260127T131000
DTSTAMP:20260622T142532
CREATED:20260106T213106Z
LAST-MODIFIED:20260106T233659Z
UID:3942-1769516100-1769519400@colleges.claremont.edu
SUMMARY:The forbidden quiver of a link (Sam Nelson\, CMC)
DESCRIPTION:Virtual links can be represented as equivalence classes of Gauss diagrams under Reidemeister moves. The Forbidden Moves are moves which look plausible but change the virtual isotopy class of the knot or link — indeed\, virtual knots are all trivial if we allow forbidden moves. However\, virtual links remain non-trivial. In this talk we show how to think of these links as quivers and in the process\, define several polynomial invariants of link homotopy. This is joint work with Stella Shah (Scripps College).
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-sam-nelson-cmc-4/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20251202T121500
DTEND;TZID=America/Los_Angeles:20251202T131000
DTSTAMP:20260622T142532
CREATED:20250808T202734Z
LAST-MODIFIED:20251120T202437Z
UID:3778-1764677700-1764681000@colleges.claremont.edu
SUMMARY:Positivity aspects of complete homogeneous symmetric polynomials (Stephan Garcia\, Pomona)
DESCRIPTION:Hunter’s theorem ensures that the complete homogeneous symmetric (CHS) polynomials of even degree are positive definite functions.  We provide new proofs of Hunter’s theorem\, applications to operator theory\, and a noncommutative (NC) generalization that sheds light even on the commutative case.  Surprisingly\, this work emerged from a problem in analytic combinatorics.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-stephan-garcia-pomona-2/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20251118T121500
DTEND;TZID=America/Los_Angeles:20251118T131000
DTSTAMP:20260622T142532
CREATED:20250808T232856Z
LAST-MODIFIED:20251113T200129Z
UID:3779-1763468100-1763471400@colleges.claremont.edu
SUMMARY:Non-vanishing of L-functions over function fields (Alexandra Florea\, UC Irvine)
DESCRIPTION:I will talk about some results concerning the non-vanishing of $L$-functions associated to fixed order characters $\ell$ at the central point over functions fields. Quadratic characters have been studied a lot over the years\, and very good non-vanishing results are available in this case\, due to work of Soundararajan. When focusing on cubic and higher order characters\, much less is known. In this talk\, I will explain how one can obtain a positive proportion of non-vanishing for any fixed order $\ell$ characters\, which goes to $0$ as $\ell$ goes to infinity. This is based on joint work with C. David and M. Lalin.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-alexandra-florea-uc-irvine/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20251111T121500
DTEND;TZID=America/Los_Angeles:20251111T131000
DTSTAMP:20260622T142532
CREATED:20250827T221608Z
LAST-MODIFIED:20251022T171318Z
UID:3799-1762863300-1762866600@colleges.claremont.edu
SUMMARY:Elementary probability via bundles (Wai Yan Pong\, Cal State Dominguez Hills)
DESCRIPTION:This talk explores elementary probability and statistics through the language of category theory. We introduce a category of Bundles and use it to reinterpret several results typically covered in an introductory course on probability and statistics. This approach naturally reveals the underlying geometric structures common to these results. The talk is accessible to anyone familiar with linear algebra\, and we hope teachers of probability will find this perspective fresh and interesting.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-wai-yan-pong-cal-state-dominguez-hills-2/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20251104T121500
DTEND;TZID=America/Los_Angeles:20251104T131000
DTSTAMP:20260622T142532
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:20260622T142532
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:20260622T142532
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:20260622T142532
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:20260622T142532
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:20260622T142532
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:20260622T142532
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:20260622T142532
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:20241203T150000
DTEND;TZID=America/Los_Angeles:20241203T160000
DTSTAMP:20260622T142532
CREATED:20240928T045355Z
LAST-MODIFIED:20241202T162645Z
UID:3555-1733238000-1733241600@colleges.claremont.edu
SUMMARY:Claremont Topology Seminar: Rhea Palak Bakshi (University of California\, Santa Barbara)
DESCRIPTION:We welcome all undergraduate/graduate students and faculty to attend topology seminar! \nSpeaker: Rhea Palak Bakshi (University of California Santa Barbara) \nTitle: The skein module of the connected sum of two copies of L(0\,1) \nAbstract: Abstract: Skein modules were introduced by Jozef H. Przytycki\, and independently by Vladmimor Turaev\, as generalisations of the Jones\, Kauffman bracket\, and HOMFLYPT polynomial link invariants in the 3-sphere to arbitrary 3-manifolds. The Kauffman bracket skein module (KBSM) is the most extensively studied of all. However\, computing the KBSM of a 3-manifold is known to be notoriously hard\, especially over the ring of Laurent polynomials. Marche conjectured that over the ring of Laurent polynomials\, the KBSM of closed oriented 3-manifolds splits into the sum of free and torsion modules. The counterexample to this conjecture is given by the connected sum of two copies of the real projective space. With the goal of finding a definite structure of the KBSM over this ring\, we compute the skein module of S^1 x S^2 # H_1 and S^1 x S^2 # S^1 x S^2. We show that it is isomorphic to the KBSM of a genus two handlebody modulo some specific handle sliding relations. Moreover\, these handle sliding relations can be written in terms of Chebyshev polynomials. We also discuss whether the KBSM of these manifolds splits into the sums of free and torsion modules. This is joint work with Seongjeong Kim\, Shangjun Shi\, and Xiao Wang.
URL:https://colleges.claremont.edu/ccms/event/claremont-topology-seminar-rhea-palak-bakshi-university-of-california-santa-barbara/
LOCATION:Estella 2099
CATEGORIES:Topology Seminar
ORGANIZER;CN="Bahar Acu":MAILTO:Bahar_Acu@pitzer.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241112T150000
DTEND;TZID=America/Los_Angeles:20241112T160000
DTSTAMP:20260622T142532
CREATED:20240928T045117Z
LAST-MODIFIED:20241109T013611Z
UID:3553-1731423600-1731427200@colleges.claremont.edu
SUMMARY:Claremont Topology Seminar: Claudio Gomez-Gonzales (Carleton College - UC Irvine)
DESCRIPTION:We welcome all undergraduate/graduate students and faculty to attend the Topology Seminar! \nSpeaker: Claudio Gomez-Gonzales (Carleton College – UC Irvine) \nTitle: How hard could it be? A tour of resolvent degree \nAbstract: Solving algebraic equations are among the oldest problems in mathematics. In this talk\, we offer a concrete\, visual\, and historical introduction to resolvent degree (RD)\, an invariant that aspires to quantify just how hard these problems are. The lineage of this theory includes the origins of topology\, Klein’s “hypergalois” program\, and centuries-old exploits in reducing numbers of coefficients\, which dare us to push beyond the solvable/unsolvable dichotomy. We will build towards the notion of versality central to Klein’s vision\, with a nod to our general framework implemented in joint work with Alexander Sutherland and Jesse Wolfson\, that permits us to address resolvent questions via classical invariant theory. We will conclude by reflecting on the past and future of resolvent problems\, along with what we do and don’t know about RD. This talk is designed to be accessible for undergraduates—let’s do some math!
URL:https://colleges.claremont.edu/ccms/event/claremont-topology-seminar-claudio-gomez-gonzales-carleton-college-uc-irvine/
LOCATION:Estella 2099
CATEGORIES:Topology Seminar
ORGANIZER;CN="Bahar Acu":MAILTO:Bahar_Acu@pitzer.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241105T150000
DTEND;TZID=America/Los_Angeles:20241105T160000
DTSTAMP:20260622T142532
CREATED:20240928T045017Z
LAST-MODIFIED:20241025T175032Z
UID:3550-1730818800-1730822400@colleges.claremont.edu
SUMMARY:Claremont Topology Seminar: Vijay Higgins (UCLA)
DESCRIPTION:We welcome all undergraduate/graduate students and faculty to attend topology seminar! \nSpeaker: Vijay Higgins (UCLA) \nTitle: Webs and skein algebras \nAbstract: The Jones polynomial of a link can be computed diagrammatically by using skein relations\, which encode the representation theory of SL(2). By considering the vector space spanned by links drawn on a surface and imposing these skein relations\, we obtain an algebra known as the Kauffman bracket skein algebra of the surface. These algebras have been studied by many authors\, including F. Bonahon and H. Wong\, and much is known about their structure. Replacing SL(2) by SL(3) or any other higher rank Lie group gives rise to a new skein algebra involving not only links but also certain graphs called webs. In this talk\, we will discuss some of the complications involved with studying skein algebras built from webs on surfaces and then present ways of getting around them. Some of this work is joint with F. Bonahon.
URL:https://colleges.claremont.edu/ccms/event/claremont-topology-seminar-vijay-higgins-ucla/
LOCATION:Estella 2099
CATEGORIES:Topology Seminar
ORGANIZER;CN="Bahar Acu":MAILTO:Bahar_Acu@pitzer.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241029T150000
DTEND;TZID=America/Los_Angeles:20241029T160000
DTSTAMP:20260622T142532
CREATED:20240928T044917Z
LAST-MODIFIED:20241024T185135Z
UID:3552-1730214000-1730217600@colleges.claremont.edu
SUMMARY:Claremont Topology Seminar: Orsola Capovilla-Searle (UC Davis)
DESCRIPTION:We welcome all undergraduate/graduate students and faculty to attend topology seminar! \nSpeaker: Orsola Capovilla-Searle (UC Davis) \nTitle: Exact Lagrangian fillings of Legendrian links \nAbstract: An important problem in contact topology is to understand Legendrian submanifolds; these submanifolds are always tangent to the plane field given by the contact structure. Legendrian links arise as wavefronts in optics\, and can sometimes be used to distinguish contact structures. Legendrian links can also arise as the boundary of exact Lagrangian surfaces in the standard symplectic 4-ball which are called fillings of the link. In the last seven years\, our understanding of the moduli space of fillings for various families of Legendrians has greatly improved thanks to tools from sheaf theory\, Floer theory and cluster algebras. I will talk about recent work establishing connections between fillings and Newton polytopes\, as well as applications to higher dimensional Legendrian submanifolds and non-orientable fillings.
URL:https://colleges.claremont.edu/ccms/event/claremont-topology-seminar-orsola-capovilla-searle-uc-davis-2/
LOCATION:Estella 2099
CATEGORIES:Topology Seminar
ORGANIZER;CN="Bahar Acu":MAILTO:Bahar_Acu@pitzer.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241001T150000
DTEND;TZID=America/Los_Angeles:20241001T160000
DTSTAMP:20260622T142532
CREATED:20240928T044059Z
LAST-MODIFIED:20240928T044059Z
UID:3549-1727794800-1727798400@colleges.claremont.edu
SUMMARY:Claremont Topology Seminar: Reginald Anderson (CMC)
DESCRIPTION:We welcome all undergraduate/graduate students and faculty to attend topology seminar! \nSpeaker: Reginald Anderson (CMC) \nTitle: Presentations of derived categories \nAbstract: 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/claremont-topology-seminar-reginald-anderson-cmc-3/
LOCATION:Estella 2099
CATEGORIES:Topology Seminar
ORGANIZER;CN="Bahar Acu":MAILTO:Bahar_Acu@pitzer.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240924T121500
DTEND;TZID=America/Los_Angeles:20240924T131000
DTSTAMP:20260622T142532
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:20240917T150000
DTEND;TZID=America/Los_Angeles:20240917T160000
DTSTAMP:20260622T142532
CREATED:20240906T122404Z
LAST-MODIFIED:20240906T122541Z
UID:3496-1726585200-1726588800@colleges.claremont.edu
SUMMARY:Claremont Topology Seminar: Migiwa Sakurai (Shibaura Institute of Technology)
DESCRIPTION:We welcome all undergraduate/graduate students and faculty to attend topology seminar! \nSpeaker: Migiwa Sakurai (Shibaura Institute of Technology) \nTitle: Clasp pass moves and arrow polynomials of virtual knots \nAbstract: For classical knots\, clasp pass moves are closely related to Vassiliev invariants of degree 3. Tsukamoto showed that the values of the Vassiliev invariant of degree 3 induced from the Jones polynomial for two knots differ by 0 or +36/-36\, if they are related by a single clasp pass move. For virtual knots\, the arrow polynomial is a generalization of the Jones polynomial and induces a Vassiliev invariant of degree 3. We show that the values of the Vassiliev invariant of degree 3 induced from the arrow polynomial of two virtual knots differ by 0 or +2304/-2304\, if they are related by a single clasp pass move. We also obtain a lower bound of the distance between virtual knots by clasp pass moves.
URL:https://colleges.claremont.edu/ccms/event/claremont-topology-seminar-migiwa-sakurai-shibaura-institute-of-technology/
LOCATION:Estella 2099
CATEGORIES:Topology Seminar
ORGANIZER;CN="Bahar Acu":MAILTO:Bahar_Acu@pitzer.edu
END:VEVENT
END:VCALENDAR