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DTSTART;TZID=America/Los_Angeles:20220215T123000
DTEND;TZID=America/Los_Angeles:20220215T132000
DTSTAMP:20260425T074919
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:20260425T074919
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:20260425T074919
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:20260425T074919
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:20260425T074919
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:20260425T074919
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:20260425T074919
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:20260425T074919
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:20260425T074919
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:20260425T074919
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:20260425T074919
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:20260425T074919
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:20260425T074919
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:20260425T074919
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:20260425T074919
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
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20210907T123000
DTEND;TZID=America/Los_Angeles:20210907T132000
DTSTAMP:20260425T074919
CREATED:20210823T221435Z
LAST-MODIFIED:20210830T213551Z
UID:2214-1631017800-1631020800@colleges.claremont.edu
SUMMARY:Region colorings in knot theory (Sam Nelson\, CMC)
DESCRIPTION:In this talk we will survey recent developments in the use of ternary algebraic structures known as Niebrzydowski Tribrackets in defining invariants of knots\, with some perhaps surprising applications.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-sam-nelson-cmc/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20210831T123000
DTEND;TZID=America/Los_Angeles:20210831T132000
DTSTAMP:20260425T074919
CREATED:20210823T222615Z
LAST-MODIFIED:20210829T182033Z
UID:2216-1630413000-1630416000@colleges.claremont.edu
SUMMARY:Representing integers by multilinear polynomials (Lenny Fukshansky\, CMC)
DESCRIPTION:Given a homogeneous multilinear polynomial F(x) in n variables with integer coefficients\, we obtain some sufficient conditions for it to represent all the integers. Further\, we derive effective results\, establishing bounds on the size of a solution x to the equation F(x) = b\, where b is any integer. For a special class of polynomials coming from determinants of rectangular matrices we are able to obtain necessary and sufficient conditions for such an effective representation problem. This result naturally connects to the problem of extending a collection of primitive vectors to a basis in a lattice\, where we present counting estimates on the number of such extensions. Equivalently\, this can be described as the number of ways a rectangular integer matrix can be extended to a matrix in GL_n(Z)\, when such extensions are possible. The talk is based on joint works with A. Boettcher and with M. Forst.
URL:https://colleges.claremont.edu/ccms/event/representing-integers-by-multilinear-polynomials-lenny-fukshansky-cmc/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
END:VCALENDAR