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DTSTART;TZID=America/Los_Angeles:20221011T121500
DTEND;TZID=America/Los_Angeles:20221011T131000
DTSTAMP:20260627T101935
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:20260627T101935
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:20260627T101935
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:20260627T101935
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:20260627T101935
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:20260627T101935
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:20260627T101935
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
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220426T123000
DTEND;TZID=America/Los_Angeles:20220426T132000
DTSTAMP:20260627T101935
CREATED:20220127T053038Z
LAST-MODIFIED:20220421T192843Z
UID:2570-1650976200-1650979200@colleges.claremont.edu
SUMMARY:Bounds for nonzero Littlewood-Richardson coefficients (Müge Taskin\, Boğaziçi University\, Turkey)
DESCRIPTION:As  $\lambda$ runs through all integer partitions\, the set of   Schur functions $\{s_{\lambda}\}_\lambda$ forms a basis in the ring of symmetric functions. Hence the rule $$s_{\lambda}s_{\mu}=\sum c_{\lambda\,\mu}^{\gamma} s_{\gamma}$$ makes sense and the coefficients $c_{\lambda\,\mu}^{\gamma}$ are called \textit{Littlewood-Richardson (LR) coefficients}. The calculations of Littlewood-Richardson coefficients has been an important problem from the first time they were introduced\, due to their important role in representation theory of symmetric groups and enumerative geometry. \nIn this talk we will explain some of the main features of these coefficients and provide a summary of the characterizations given by Littlewood and Richardson (1934)\, Berenstein- Zelevinsky ()1988) and Knutson-Tao (1999). Then we will explain our approach to a seemingly easier problem\, that is\, the determination of  triples $(\lambda\,\mu\,\gamma)$  of partitions for which $c_{\lambda\,\mu}^{\gamma}$ is non zero. Our method describes some upper and lower bounds for triples $(\lambda\,\mu\,\gamma)$ with nonzero  $c_{\lambda\,\mu}^{\gamma}$\, by using  Young diagram combinatorics and especially\, the indispensable Dominance order. This is joint work with R. Bedii Gümüş and supported by Tübitak/1001/115F156.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-muge-taskin-bogazici-university-turkey/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220419T123000
DTEND;TZID=America/Los_Angeles:20220419T132000
DTSTAMP:20260627T101935
CREATED:20220124T234622Z
LAST-MODIFIED:20220413T160024Z
UID:2553-1650371400-1650374400@colleges.claremont.edu
SUMMARY:A conjugacy criterion for two pairs of 2 x 2 matrices over a commutative ring (Bogdan Petrenko\, Eastern Illinois University)
DESCRIPTION:I will explain how to apply presentations of algebras (together with some classical results from non-commutative algebra) to obtain some 5 polynomial invariants telling us when two pairs of 2×2 matrices over a commutative ring are conjugate\, assuming that each of these pairs generate the matrix algebra. This talk is based on my joint paper with Marcin Mazur (Binghamton University):  Separable algebras over infinite fields are 2-generated and finitely presented\, Arch. Math. 93 (2009)\, 521-529.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-bogdan-petrenko-eastern-illinois-university/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220412T123000
DTEND;TZID=America/Los_Angeles:20220412T132000
DTSTAMP:20260627T101935
CREATED:20211213T015630Z
LAST-MODIFIED:20220225T220354Z
UID:2510-1649766600-1649769600@colleges.claremont.edu
SUMMARY:Geometrization of Markov numbers (Oleg Karpenkov\, University of Liverpool)
DESCRIPTION:In this talk we link discrete Markov spectrum to geometry of continued fractions. As a result of that we get a natural generalization of classical Markov tree which leads to an efficient computation of Markov minima for all elements in generalized Markov trees.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-oleg-karpenkov-university-of-liverpool/
LOCATION:TBA
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220405T123000
DTEND;TZID=America/Los_Angeles:20220405T132000
DTSTAMP:20260627T101935
CREATED:20220125T062030Z
LAST-MODIFIED:20220326T052025Z
UID:2556-1649161800-1649164800@colleges.claremont.edu
SUMMARY:Covering by polynomial planks (Alexey Glazyrin\, University of Texas Rio Grande Valley)
DESCRIPTION:In 1932\, Tarski conjectured that a convex body of width 1 can be covered by planks\, regions between two parallel hyperplanes\, only if the total width of planks is at least 1. In 1951\, Bang proved the conjecture of Tarski. In this work we study the polynomial version of Tarski’s plank problem. \nWe note that the recent polynomial proofs of the spherical and complex plank covering problems by Zhao and Ortega-Moreno give some general information on zeros of real and complex polynomials restricted to the unit sphere. As a corollary of these results\, we establish several generalizations of the Bang plank covering theorem.\nUsing the polynomial approach\, we also prove the strengthening of the Fejes Tóth zone conjecture on covering a sphere by spherical segments\, closed parts of the sphere between two parallel hyperplanes. In particular\, we show that the sum of angular widths of spherical segments covering the whole sphere is at least π. \nThis is a joint work with Roman Karasev and Alexandr Polyanskii.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-alexey-glazyrin-university-of-texas-rio-grande-valley/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220329T123000
DTEND;TZID=America/Los_Angeles:20220329T132000
DTSTAMP:20260627T101935
CREATED:20220127T202631Z
LAST-MODIFIED:20220326T051329Z
UID:2573-1648557000-1648560000@colleges.claremont.edu
SUMMARY:Peg solitaire in multiple colors on graphs (Tara Davis\, Hawaii Pacific University and Roberto Soto\, Cal State Fullerton)
DESCRIPTION:Peg solitaire is a popular one person board game that has been played in many countries on various board shapes. Recently\, peg solitaire has been studied extensively in two colors on mathematical graphs. We will present our rules for multiple color peg solitaire on graphs. We will present some student and faculty results classifying the solvability of the game on several graceful graphs\, as well as discuss open questions.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-tara-davis-hawaii-pacific-university-and-roberto-soto-cal-state-fullerton/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220322T123000
DTEND;TZID=America/Los_Angeles:20220322T132000
DTSTAMP:20260627T101935
CREATED:20220128T031313Z
LAST-MODIFIED:20220321T182413Z
UID:2575-1647952200-1647955200@colleges.claremont.edu
SUMMARY:Continuous extensions of Ramanujan-expandable arithmetic functions (Matthew Fox\, Perimeter Institute for Theoretical Physics and Chai Karamchedu\, Sandia National Labs)
DESCRIPTION:We describe a natural way to continuously extend arithmetic functions that admit a Ramanujan expansion and derive the conditions under which such an extension exists. In particular\, we show that the absolute convergence of a Ramanujan expansion does not guarantee the convergence of its real variable generalization. We take the divisor function as a case study\, and consider how to continuously extend it to the reals.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-matthew-fox-perimeter-institute-for-theoretical-physics-and-chai-karamchedu-sandia-national-labs/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220308T123000
DTEND;TZID=America/Los_Angeles:20220308T132000
DTSTAMP:20260627T101935
CREATED:20220112T041154Z
LAST-MODIFIED:20220222T011851Z
UID:2527-1646742600-1646745600@colleges.claremont.edu
SUMMARY:Equidistribution of norm 1 elements in cyclic number fields (Kate Petersen\, University of Minnesota Duluth)
DESCRIPTION:By Hilbert’s theorem 90\, if K is a cyclic number field with Galois group generated by g\, then any element of norm 1 can be written as a/g(a).  This gives rise to a natural height function on elements of norm 1.  I’ll discuss equidistribution problems and show that these norm 1 elements are equidistributed (in an appropriate quotient) with respect to this height.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-kate-petersen-university-of-minnesota-duluth/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220301T123000
DTEND;TZID=America/Los_Angeles:20220301T132000
DTSTAMP:20260627T101935
CREATED:20220111T231348Z
LAST-MODIFIED:20220221T211055Z
UID:2524-1646137800-1646140800@colleges.claremont.edu
SUMMARY:Gap theorems for linear forms and for rotations on higher dimensional tori (Alan Haynes\, University of Houston)
DESCRIPTION:This talk is based on joint work with Jens Marklof\, and with Roland Roeder. The three distance theorem states that\, if x is any real number and N is any positive integer\, the points x\, 2x\, … \, Nx modulo 1 partition the unit interval into component intervals having at most 3 distinct lengths. We will present two higher dimensional analogues of this problem. In the first we consider points of the form mx+ny modulo 1\, where x and y are real numbers and m and n are integers taken from an expanding set in the plane. This version of the problem was previously studied by Geelen and Simpson\, Chevallier\, Erdős\, and many other people\, and it is closely related to the Littlewood conjecture in Diophantine approximation. The second version of the problem is a straightforward generalization to rotations on higher dimensional tori which\, surprisingly\, has been mostly overlooked in the literature. For the two dimensional torus\, we are able to prove a five distance theorem\, which is best possible. In higher dimensions we also have bounds\, but establishing optimal bounds is an open problem.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-alan-haynes-university-of-houston/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220215T123000
DTEND;TZID=America/Los_Angeles:20220215T132000
DTSTAMP:20260627T101935
CREATED:20220119T153839Z
LAST-MODIFIED:20220210T023821Z
UID:2540-1644928200-1644931200@colleges.claremont.edu
SUMMARY:Recent trends in using representations in voting theory - committees and cyclic orders (Karl-Dieter Crisman\, Gordon College)
DESCRIPTION:One of the most important axioms in analyzing voting systems is that of “neutrality”\, which stipulates that the system should treat all candidates symmetrically. Even though this doesn’t always directly apply (such as in primary systems or those with intentional incumbent protection)\, it is extremely important both in theory and practice.If the voting systems in question additionally are tabulated using some sort of points\, we can translate the notion of neutrality into invariance under an action of the symmetric group on a vector space. This means we can exploit representation theory to analyze them\, and this has been successfully done in a number of social choice contexts from cooperative games to voting on full rankings.In this talk\, we describe recent progress in extending this technique to two interesting situations. First we consider work of Barcelo et al. on voting for committees of representatives (such as for departments in a college)\, where the wreath product of two symmetric groups comes into play. Then we look at work by Crisman et al. regarding voting on “cyclic orders”\, or ways to seat people around a table\, which implicitly has both left and right actions of the symmetric group to consider.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-karl-dieter-crisman-gordon-college/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220208T123000
DTEND;TZID=America/Los_Angeles:20220208T132000
DTSTAMP:20260627T101935
CREATED:20220131T003643Z
LAST-MODIFIED:20220131T003643Z
UID:2585-1644323400-1644326400@colleges.claremont.edu
SUMMARY:Frame coherence and nearly orthogonal lattices (Lenny Fukshansky\, CMC)
DESCRIPTION:A frame in a Euclidean space is a spanning set\, which can be overdetermined. Large frames are used for redundant signal transmission\, which allows for error correction. An important parameter of frames is coherence\, which is maximal absolute value of the cosine of the angle between two frame vectors: the smaller it is\, the closer is the frame to being orthogonal\, which minimizes noise from overlapping frequencies in transmission. One good source frames with sufficiently low coherence comes from layers of minimal vectors in a lattice. We will discuss a particular class of so-called nearly orthogonal lattices\, which exhibits some interesting properties from the stand-point of coherence and other related optimization problems. This is joint work with David Kogan (CGU).
URL:https://colleges.claremont.edu/ccms/event/frame-coherence-and-nearly-orthogonal-lattices-lenny-fukshansky-cmc/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220201T123000
DTEND;TZID=America/Los_Angeles:20220201T132000
DTSTAMP:20260627T101935
CREATED:20220121T001428Z
LAST-MODIFIED:20220126T183034Z
UID:2543-1643718600-1643721600@colleges.claremont.edu
SUMMARY:Niho's last conjecture (Daniel Katz\, Cal State Northridge)
DESCRIPTION:A power permutation of a finite field F is a permutation of F whose functional form is x -> x^d for some exponent d.  Power permutations are used in cryptography\, and the exponent d must be chosen so that the permutation is highly nonlinear\, that is\, not easily approximated by linear functions.  The Walsh spectrum of a power permutation is a list of numbers measuring the correlation of our power permutation with the various linear functions. The last conjecture in Niho’s 1972 thesis considers a particular infinite family of highly nonlinear power permutations\, and states that each permutation in this family has a Walsh spectrum with at most five distinct values. Niho’s own techniques show that there are at most eight distinct values. Each of the eight candidate values corresponds to a possible number of distinct roots of a seventh degree polynomial on a subset of the finite field F called the unit circle. We use symmetry arguments to show that it is impossible to have four\, six\, or seven roots on the unit circle: this proves Niho’s last conjecture. This is joint work with Tor Helleseth and Chunlei Li.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-daniel-katz-cal-state-northridge/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220125T123000
DTEND;TZID=America/Los_Angeles:20220125T132000
DTSTAMP:20260627T101935
CREATED:20210907T183748Z
LAST-MODIFIED:20220119T170851Z
UID:2308-1643113800-1643116800@colleges.claremont.edu
SUMMARY:Questions on Symmetric Chains (Shahriar Shahriari\, Pomona)
DESCRIPTION:The set of subsets {1\, 3}\, {1\, 3\, 4}\, {1\, 3\, 4\, 6} is a symmetric chain in the partially ordered set (poset) of subsets of {1\,…\,6}. It is a chain\, because each of the subsets is a subset of the next one. It is symmetric because the collection has as many subsets with less than 3 elements as it has subsets with more than 3 elements (3 is half of 6\, the size of the original set). It is straightforward to partition the set of all subsets of {1\,…\,6} into symmetric chains. Such a partition is called a symmetric chain decomposition of the poset. We are interested in the following—admittedly curious sounding—question. What is the maximum integer k\, such that given any collection of k disjoint symmetric chains in the poset of subsets of a finite set\, we can enlarge the collection to a symmetric chain decomposition of the poset? I don’t know the answer\, but in this talk\, I will discuss a special case\, a number of related results and questions\, and provide some background on why symmetric chain decompositions are useful.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-shahriar-shahriari-pomona/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20211207T123000
DTEND;TZID=America/Los_Angeles:20211207T132000
DTSTAMP:20260627T101935
CREATED:20210907T183311Z
LAST-MODIFIED:20211130T221522Z
UID:2304-1638880200-1638883200@colleges.claremont.edu
SUMMARY:Difference sets in higher dimensions (David Conlon\, Cal Tech)
DESCRIPTION:Let d >= 2 be a natural number. We determine the minimum possible size of the difference set A-A in terms of |A| for any sufficiently large finite subset A of R^d that is not contained in a translate of a hyperplane. By a construction of Stanchescu\, this is best possible and thus resolves an old question first raised by Uhrin. Joint work with Jeck Lim.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-david-conlon-cal-tech/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20211130T123000
DTEND;TZID=America/Los_Angeles:20211130T132000
DTSTAMP:20260627T101935
CREATED:20210819T183424Z
LAST-MODIFIED:20211118T191414Z
UID:2203-1638275400-1638278400@colleges.claremont.edu
SUMMARY:Odd subgraphs are odd (Asaf Ferber\, UC Irvine)
DESCRIPTION:In this talk we discuss some problems related to finding large induced subgraphs of a given graph G which satisfy some degree-constraints (for example\, all degrees are odd\, or all degrees are j mod k\, etc). We survey some classical results\, present some interesting and challenging problems\, and sketch solutions to some of them. This is based on joint works with Michael Krivelevich\, and with Liam Hardiman and Michael Krivelevich.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-asaf-ferber-uc-irvine/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20211116T123000
DTEND;TZID=America/Los_Angeles:20211116T132000
DTSTAMP:20260627T101935
CREATED:20210821T181311Z
LAST-MODIFIED:20211101T170121Z
UID:2206-1637065800-1637068800@colleges.claremont.edu
SUMMARY:On sparse representation of vectors in lattices and semigroups (Iskander Aliev\, Cardiff University)
DESCRIPTION:We will discuss the sparsity of the solutions to systems of linear Diophantine equations with and without non-negativity constraints. The sparsity of a solution vector is the number of its nonzero entries\, which is referred to as the 0-norm of the vector. Our main results are new improved bounds on the minimal 0-norm of solutions to systems Ax=b\, where A is an integer matrix\, b is an integer vector and x is either a general integer vector (lattice case) or a non-negative integer vector (semigroup case). The talk is based on a joint work with G. Averkov\, J. A. De Loera and T. Oertel.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-iskander-aliev-cardiff-university/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20211109T123000
DTEND;TZID=America/Los_Angeles:20211109T132000
DTSTAMP:20260627T101935
CREATED:20210825T201712Z
LAST-MODIFIED:20211101T172659Z
UID:2218-1636461000-1636464000@colleges.claremont.edu
SUMMARY:The Chow ring of heavy/light Hassett spaces via tropical geometry (Dagan Karp\, HMC)
DESCRIPTION:Hassett spaces in genus 0 are moduli spaces of weighted pointed stable rational curves; they are important in the minimal model program and enumerative geometry. We compute the Chow ring of heavy/light Hassett spaces. The computation involves intersection theory on the toric variety corresponding to a graphic matroid\, and rests upon the work of Cavalieri-Hampe-Markwig-Ranganathan. This is joint work with Siddarth Kannan and Shiyue Li.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-dagan-karp-hmc/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20211102T123000
DTEND;TZID=America/Los_Angeles:20211102T132000
DTSTAMP:20260627T101935
CREATED:20210826T052223Z
LAST-MODIFIED:20211025T185715Z
UID:2221-1635856200-1635859200@colleges.claremont.edu
SUMMARY:Counting points in discrete subgroups (Jeff Vaaler\, UT Austin)
DESCRIPTION:We consider the problem of comparing the number of discrete points that belong to a set with the measure (or volume) of the set\, under circumstances where we expect these two numbers to be approximately equal. We start with a locally compact\, abelian\, topological group G. We assume that G has a countably infinite\, torsion free\, discrete subgroup H. But to make the talk easier to follow we will mostly consider the case G = R^N and H = Z^N. If E ⊆ R^N is a subset there are many situations where one expects that the (finite\, positive) number Vol_N (E) is approximately equal to the cardinality |E ∩ Z^N |. We will sketch the proof of a general result that bounds the difference between these quantities. If k is an algebraic number field and k_A is the ring of adeles associated to k\, this general result is useful when G = k_A^N and H = k^N .
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-jeff-vaaler-ut-austin/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20211026T123000
DTEND;TZID=America/Los_Angeles:20211026T132000
DTSTAMP:20260627T101935
CREATED:20210822T191915Z
LAST-MODIFIED:20211024T022430Z
UID:2210-1635251400-1635254400@colleges.claremont.edu
SUMMARY:Damerell's theorem: p-adic version\, supersingular case (Pavel Guerzhoy\, University of Hawaii)
DESCRIPTION:It is widely believed that Weierstrass ignored Eisenstein’s theory of elliptic functions and developed an alternative treatment\, which is now standard\, because of a convergence issue. In particular\, the Eisenstein series of weight two does not converge absolutely while Eisenstein’s theory assigned a value to this series.\n\nIt is now well-known that the quantity which Eisentsein assigned to this series is not only correct\, but it has interesting interpretations and attracted much attention. It has been proved by Damerell in 1970 that this quantity is an algebraic number if the underlying elliptic curve has complex multiplication.\n\nIn 1976\, N. Katz interpreted Damerell’s theorem in terms of DeRham cohomology; that allowed for a p-adic approach to this algebraic number. This p-adic version of Damerell’s theorem was instrumental in Katz’s theory of p-adic modular forms and p-adic L-functions of CM-fields. The approach\, by design\, works for those primes which split in the CM-field.\n\nIn this talk\, we offer a modification of Katz’ p-adic approach to the weight two Eisenstein series which works uniformly well for all primes of good reduction\, both inert and splitting in the CM-field.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-pavel-guerzhoy-university-of-hawaii-2/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20211012T123000
DTEND;TZID=America/Los_Angeles:20211012T132000
DTSTAMP:20260627T101935
CREATED:20210831T181118Z
LAST-MODIFIED:20211006T002703Z
UID:2267-1634041800-1634044800@colleges.claremont.edu
SUMMARY:New norms on matrices induced by polynomials (Angel Chavez\, Pomona)
DESCRIPTION:The complete homogeneous symmetric (CHS) polynomials can be used to define a  family of norms on Hermitian matrices. These ‘CHS norms’ are peculiar in the sense that they depend only on the eigenvalues of a matrix and not its singular values (as opposed to the Ky-Fan and Schatten norms). We will first give a general overview behind the construction of these norms (as well as their extensions to all n x n complex matrices). The construction and validation of these norms will take us on a tour of probability theory\, convexity analysis\, partition combinatorics and trace polynomials in noncommuting variables. We then discuss open problems and potential for future work. This talk is based on joint work with Konrad Aguilar\, Stephan Garcia and Jurij Volčič.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-angel-chavez-pomona/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20211005T123000
DTEND;TZID=America/Los_Angeles:20211005T132000
DTSTAMP:20260627T101935
CREATED:20210906T215040Z
LAST-MODIFIED:20210906T215040Z
UID:2301-1633437000-1633440000@colleges.claremont.edu
SUMMARY:Critical points of toroidal Belyi maps (Edray Goins\, Pomona)
DESCRIPTION:A Belyi map $\beta: \mathbb{P}^1(\mathbb{C}) \to \mathbb{P}^1(\mathbb{C})$ is a rational function with at most three critical values; we may assume these values are $\{ 0\, \\, 1\, \\, \infty \}$.  Replacing $\mathbb{P}^1$ with an elliptic curve $E: \ y^2 = x^3 + A \\, x + B$\, there is a similar definition of a Belyi map $\beta: E(\mathbb{C}) \to \mathbb{P}^1(\mathbb{C})$.  Since $E(\mathbb{C}) \simeq \mathbb T^2(\mathbb {R})$ is a torus\, we call $(E\, \beta)$ a Toroidal \Belyi pair. \n\n\nThere are many examples of Belyi maps $\beta: E(\mathbb{C}) \to \mathbb P^1(\mathbb{C})$ associated to elliptic curves; several can be found online at LMFDB. Given such a Toroidal Belyi map of degree $N$\, the inverse image $G = \beta^{-1} \bigl( \{ 0\, \\, 1\, \\, \infty \} \bigr)$ is a set of $N$ elements which contains the critical points of the \Belyi map. In this project\, we investigate when $G$ is contained in $E(\mathbb{C})_{\text{tors}}$. \n\n\nThis is work done as part of the Pomona Research in Mathematics Experience (NSA H98230-21-1-0015).
URL:https://colleges.claremont.edu/ccms/event/critical-points-of-toroidal-belyi-maps-edray-goins-pomona/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20210928T123000
DTEND;TZID=America/Los_Angeles:20210928T132000
DTSTAMP:20260627T101935
CREATED:20210827T004513Z
LAST-MODIFIED:20210921T181604Z
UID:2224-1632832200-1632835200@colleges.claremont.edu
SUMMARY:An algebraic introduction to the Kauffman bracket skein algebra (Helen Wong\, CMC)
DESCRIPTION:The Kauffman bracket skein algebra was originally defined as a generalization of the Jones polynomial for knots and links on a surface and is one of the few quantum invariants where the connection to hyperbolic geometry is fairly well-established.  Explicating this connection to hyperbolic geometry requires an understanding of the non-commutative structure of the skein algebra\, especially at roots of unity.  We’ll present some of the known (and not known) properties of the skein algebra.  Highlights include the Chebyshev polynomials\, quantum tori\, $SL(2\, \mathbb C)$ and other interesting algebraic objects.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-helen-wong-cmc/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20210921T123000
DTEND;TZID=America/Los_Angeles:20210921T131000
DTSTAMP:20260627T101935
CREATED:20210831T205637Z
LAST-MODIFIED:20210906T215314Z
UID:2272-1632227400-1632229800@colleges.claremont.edu
SUMMARY:The magic of the number three: three explanatory proofs in abstract algebra (Gizem Karaali\, Pomona)
DESCRIPTION:When first learning how to write mathematical proofs\, it is often easier for students to work with statements using the universal quantifier. Results that single out special cases might initially come across as more puzzling or even mysterious. Explanatory proofs\, in the sense of Steiner\, transform what might initially seem mysterious or even magical into lucid mathematics. In this talk we explore three specific statements from abstract algebra that involve the number three\, whose proofs are explanatory. This is joint work with Samuel Yih PO’18.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-gizem-karaali-pomona/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20210914T123000
DTEND;TZID=America/Los_Angeles:20210914T132000
DTSTAMP:20260627T101935
CREATED:20210822T191624Z
LAST-MODIFIED:20210829T182323Z
UID:2208-1631622600-1631625600@colleges.claremont.edu
SUMMARY:On Hermite's problem\, Jacobi-Perron type algorithms\, and Dirichlet groups (Oleg Karpenkov\, Liverpool)
DESCRIPTION:In this talk we introduce a new modification of the Jacobi-Perron algorithm in the three dimensional case. This algorithm is periodic for the case of totally-real conjugate cubic vectors. To the best of our knowledge this is the first Jacobi-Perron type algorithm for which the cubic periodicity is proven. This provides an answer in the totally-real case to the question of algebraic periodicity for cubic irrationalities posed in 1848 by Ch.Hermite. \nWe will briefly discuss a new approach which is based on geometry of numbers. In addition we point out one important application of Jacobi-Perron type algorithms to the computation of independent elements in the maximal groups of commuting matrices of algebraic irrationalities.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-pavel-guerzhoy-university-of-hawaii/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
END:VCALENDAR