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DTSTART;TZID=America/Los_Angeles:20190129T121500
DTEND;TZID=America/Los_Angeles:20190129T131000
DTSTAMP:20181130T222530Z
CREATED:20181130T222530Z
LAST-MODIFIED:20181130T222530Z
UID:961-1548764100-1548767400@colleges.claremont.edu
SUMMARY:Discrete compressed sensing: lattices and frames (Josiah Park\, Georgia Tech)
DESCRIPTION:Lattice valued vector systems have taken an important role in packing\, coding\, cryptography\, and signal processing problems.  In compressed sensing\, improvements in sparse recovery methods can be reached with an additional  assumption that the signal of  interest is lattice  valued\, as demonstrated by A.  Flinth  and G. Kutyniok. Equiangular  tight  frames are  particular systems  of unit  vectors  with minimal  coherence\,  a measure of how well distributed the vectors are\, and have provable guarantees for recovery of sparse vectors in standard methods.  The determination whether real equiangular tight frames have integer span on a lattice has been given a characterization within two papers by A. Bottcher\, L. Fukshansky\, one with S. R. Garcia\, H. Maharaj and D. Needell.  Here the corresponding question is considered for the complex case and several families are demonstrated to have either integer span on a lattice or not.  In addition\, it is demonstrated that a real Parseval tight frame can have integer span on a lattice if and only if the inner products appearing in the system are rational.  (Collaboration with L. Fukshansky\, D. Needell\, and Y. Xin)
URL:https://colleges.claremont.edu/ccms/event/discrete-compressed-sensing-lattices-and-frames-josiah-park-georgia-tech/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190122T121500
DTEND;TZID=America/Los_Angeles:20190122T131000
DTSTAMP:20190113T053629Z
CREATED:20190112T013635Z
LAST-MODIFIED:20190113T053629Z
UID:1045-1548159300-1548162600@colleges.claremont.edu
SUMMARY:Niebrzydowski tribrackets and algebras (Sam Nelson\, CMC)
DESCRIPTION:In this talk we will survey recent work on Niebzydowski Tribrackets and Niebrydowski Algebras\, algebraic structures related to region colorings the planar complements of knots and trivalent spatial graphs.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-sam-nelson-cmc/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20181211T121500
DTEND;TZID=America/Los_Angeles:20181211T131000
DTSTAMP:20181205T171813Z
CREATED:20181017T000951Z
LAST-MODIFIED:20181205T171813Z
UID:915-1544530500-1544533800@colleges.claremont.edu
SUMMARY:The Bateman—Horn conjecture II:  applications (Stephan Garcia\, Pomona)
DESCRIPTION:We begin with a review of the Bateman—Horn conjecture\, which sheds light on the intimate relationship between polynomials and prime numbers.  In this expository talk\, we survey a host of applications of the conjecture.  For example\, Landau’s conjecture\, the twin prime conjecture\, and the Green—Tao theorem are all consequences of the Bateman—Horn conjecture.  Moreover\, the conjecture also illuminates the mysterious patterns observed in the Ulam spiral.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-stephan-garcia-pomona/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20181204T121500
DTEND;TZID=America/Los_Angeles:20181204T131000
DTSTAMP:20181116T225428Z
CREATED:20180817T150812Z
LAST-MODIFIED:20181116T225428Z
UID:441-1543925700-1543929000@colleges.claremont.edu
SUMMARY:Sperner's lemma: generalizations and applications (Oleg Musin\, UT Rio Grande Valley)
DESCRIPTION:The classical Sperner –  KKM (Knaster – Kuratowski – Mazurkiewicz) lemma has many applications  in combinatorics\, algorithms\, game theory and mathematical economics. In this talk we consider generalizations of this lemma as well as Gale’s colored KKM lemma and Shapley’s KKMS theorem. It is shown that spaces and covers can be much more general and the boundary KKM rules can be substituted by more weaker boundary assumptions. These generalizations of Sperner’s lemma rely on homotopy invariants of covers  that in fact are obstructions for extending a cover of a subspace A in X to a cover of  X.
URL:https://colleges.claremont.edu/ccms/event/tba-2/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20181127T121500
DTEND;TZID=America/Los_Angeles:20181127T131000
DTSTAMP:20190115T082646Z
CREATED:20181002T061007Z
LAST-MODIFIED:20190115T082646Z
UID:892-1543320900-1543324200@colleges.claremont.edu
SUMMARY:Weil sums of binomials: properties and applications (Daniel Katz\, CSUN)
DESCRIPTION:We consider sums in which an additive character of a finite field F is applied to a binomial whose individual terms (monomials) become permutations of F when regarded as functions.  These Weil sums characterize the nonlinearity of power permutations of interest in cryptography.  They also tell us about the correlation of linear recursive sequences over finite fields that are used in digital communications and remote sensing.  In these applications\, one is interested in the spectrum of Weil sum values that are obtained as the coefficients in the binomial are varied.  We discuss topics of enduring interest: Archimedean and non-Archimedean bounds on the sums\, the number of values in the spectrum\, and the presence or absence of zero in the spectrum.  We indicate some important open problems and discuss progress that has been made on them.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-talk-by-daniel-katz-csun/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20181113T121500
DTEND;TZID=America/Los_Angeles:20181113T131000
DTSTAMP:20181105T225953Z
CREATED:20180912T174329Z
LAST-MODIFIED:20181105T225953Z
UID:551-1542111300-1542114600@colleges.claremont.edu
SUMMARY:Cayley digraphs of matrix rings over finite fields (Yesim Demiroglu\, HMC)
DESCRIPTION:In this talk we use the unit-graphs and the special unit-digraphs on matrix rings to show that every n x n nonzero matrix over F_q can be written as a sum of two SL_n-matrices when n>1. We compute the eigenvalues of these graphs in terms of Kloosterman sums and study their spectral properties; and prove that if X is a subset of Mat_2 (F_q) with size |X| > (2 q^3 \sqrt{q})/(q – 1)\, then X contains at least two distinct matrices whose difference has determinant $\alpha$ for any $\alpha \in F_q^*$. Using this result we also prove a sum-product type result: if $A\,B\,C\,D \subseteq F_q$ satisfy $\sqrt[4]{|A||B||C||D|}= \Omega (q^{0.75})$ as q tends to infinity\, then $(A – B)(C – D)$ equals all of $F_q$. In particular\, if A is a subset of F_q with cardinality $|A| > \frac{3}{2} q^{3/4}$\, then the subset $(A – A) (A – A)$ equals all of $F_q$. We also recover a classical result: every element in any finite ring of odd order can be written as the sum of two units. This talk should be accessible to undergraduates with some background in linear algebra.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-by-yesim-demiroglu-hmc/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20181106T121500
DTEND;TZID=America/Los_Angeles:20181106T131000
DTSTAMP:20181102T201125Z
CREATED:20180911T214141Z
LAST-MODIFIED:20181102T201125Z
UID:537-1541506500-1541509800@colleges.claremont.edu
SUMMARY:Turning probability into polynomials (Mark Huber\, CMC)
DESCRIPTION:Moment generating functions (Laplace transforms) are a means for transforming probability problems into problems involving polynomials.  Here I will concentrate on the binomial distribution\, and use the mgf to link this distributions probabilities directly to the binomial theorem.  The mgf is also a key ingredient in Chernoff bounds\, which give upper bounds on the tail probabilities of binomial distributions (aka partial sums of the binomial theorem).  By employing the method of smoothing and tilting\, it is possible to attain bounds on the tails that go down faster than the traditional approximation heuristic that uses the Central Limit Theorem.
URL:https://colleges.claremont.edu/ccms/event/talk-by-mark-huber-cmc/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20181030T121500
DTEND;TZID=America/Los_Angeles:20181030T131000
DTSTAMP:20181024T083012Z
CREATED:20180823T224159Z
LAST-MODIFIED:20181024T083012Z
UID:471-1540901700-1540905000@colleges.claremont.edu
SUMMARY:Uniform asymptotic growth of symbolic powers  (Robert Walker\, University of Michigan)
DESCRIPTION:Algebraic geometry (AG) is a major generalization of linear algebra which is fairly influential in mathematics. Since the 1980’s with the development of computer algebra systems like Mathematica\, AG has been leveraged in areas of STEM as diverse as statistics\, robotic kinematics\, computer science/geometric modeling\, and mirror symmetry. Part one of my talk will be a brief introduction to AG\, to two notions of taking powers of ideals (regular vs symbolic) in Noetherian commutative rings\, and to the ideal containment problem that I study in my thesis. Part two of my talk will focus on stating the main results of my thesis in a user-ready form\, giving a “comical” example or two of how to use them. At the risk of sounding like Paul Rudd in Ant-Man\, I hope this talk with be awesome.
URL:https://colleges.claremont.edu/ccms/event/tba-4/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20181016T121500
DTEND;TZID=America/Los_Angeles:20181016T131000
DTSTAMP:20181008T194923Z
CREATED:20181008T194923Z
LAST-MODIFIED:20181008T194923Z
UID:897-1539692100-1539695400@colleges.claremont.edu
SUMMARY:The Bateman—Horn Conjecture\, Part I: heuristic derivation (Stephan Garcia\, Pomona)
DESCRIPTION:The Bateman—Horn Conjecture is a far-reaching statement about the distribution of the prime numbers.  It implies many known results\, such as the Green—Tao theorem\, and a variety of famous conjectures\, such as the Twin Prime Conjecture.  In this expository talk\, we start from basic principles and provide a heuristic argument in favor of the conjecture.  This talk should be accessible to undergraduates with a background in modular arithmetic.
URL:https://colleges.claremont.edu/ccms/event/the-bateman-horn-conjecture-part-i-heuristic-derivation-stephan-garcia-pomona/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20181009T121500
DTEND;TZID=America/Los_Angeles:20181009T131000
DTSTAMP:20181001T220127Z
CREATED:20180912T160739Z
LAST-MODIFIED:20181001T220127Z
UID:546-1539087300-1539090600@colleges.claremont.edu
SUMMARY:State Polytopes of Combinatorial Neural Codes (Rob Davis\, HMC)
DESCRIPTION:Combinatorial neural codes are 0/1 vectors that are used to model the co-firing patterns of a set of place cells in the brain. One wide-open problem in this area is to determine when a given code can be algorithmically drawn in the plane as a Venn diagram-like figure. A sufficient condition to do so is for the code to have a property called k-inductively pierced. Gross\, Obatake\, and Youngs recently used toric algebra to show that a code on three neurons is 1-inductively pierced if and only if the toric ideal is trivial or generated by quadratics. No result is known for additional neurons in the same generality. \nIn this talk\, we study two infinite classes of combinatorial neural codes in detail. For each code\, we explicitly compute its universal Gröbner basis. This is done for the first class by recognizing that the codewords form a Lawrence-type matrix. With the second class\, this is done by showing that the matrix is totally unimodular. These computations allow one to compute the state polytopes of the corresponding toric ideals\, from which all distinct initial ideals may be computed efficiently. Moreover\, we show that the state polytopes are combinatorially equivalent to well-known polytopes: the permutohedron and the stellohedron.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-by-rob-davis-hmc/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20181002T121500
DTEND;TZID=America/Los_Angeles:20181002T131000
DTSTAMP:20180926T151643Z
CREATED:20180911T213738Z
LAST-MODIFIED:20180926T151643Z
UID:533-1538482500-1538485800@colleges.claremont.edu
SUMMARY:An Introduction to the Sato-Tate Conjecture (Edray Goins\, Pomona College)
DESCRIPTION:In 1846\, Ernst Eduard Kummer conjectured a distribution of values of a cubic Gauss sum after computing a few values by hand.  This was forgotten about for nearly 100 years until John von Neumann and Herman Goldstine attempted to verify the conjecture as a way to test the new ENIAC machine in 1953.  They found evidence that the conjecture was false\, but trusted Kummer more than they did their digital computer.  The conjecture would hold until 1979\, when Roger Heath-Brown and Samuel Patterson proved it to be false. \nA few years earlier in 1965\, Mikio Sato and John Tate independently came up with a conjecture which gave the correct distribution of these cubic Gauss sums — although it was expressed slightly differently in terms of counting points of elliptic curves over finite fields.  In this talk\, we give an overview of the Sato-Tate Conjecture\, present an approach by Jean-Pierre Serre following his paper from 1967\, then sketch the 2006 proof of the conjecture following the ideas of Laurent Clozel\, Michael Harris\, Nicholas Shepherd-Barron and Richard Taylor. \nHere are the slides of this lecture: Edray Goins’ slides.
URL:https://colleges.claremont.edu/ccms/event/talk-by-edray-goins-pomona-college/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20180925T121500
DTEND;TZID=America/Los_Angeles:20180925T131000
DTSTAMP:20180926T151534Z
CREATED:20180911T213219Z
LAST-MODIFIED:20180926T151534Z
UID:531-1537877700-1537881000@colleges.claremont.edu
SUMMARY:Quandle coloring quivers (Sam Nelson\, CMC)
DESCRIPTION:Given a finite quandle $X$\, a set $S \subset \mathrm{Hom}(X\,X)$ of quandle endomoprhisms\, and an oriented knot or link $L$\, we construct a quiver-valued invariant of oriented knots and links. This quiver categorifies the quandle counting invariant in the most literal sense and can be used to define many enhancements of the counting invariant. This is joint work with Harvey Mudd College student Karina Cho.
URL:https://colleges.claremont.edu/ccms/event/talk-by-sam-nelson-cmc/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20180918T121500
DTEND;TZID=America/Los_Angeles:20180918T131000
DTSTAMP:20180926T174121Z
CREATED:20180822T051451Z
LAST-MODIFIED:20180926T174121Z
UID:449-1537272900-1537276200@colleges.claremont.edu
SUMMARY:Inversions for reduced words (Sami Assaf\, USC)
DESCRIPTION:The number of inversions of a permutation is an important statistic that arises in many contexts\, including as the minimum number of simple transpositions needed to express the permutation and\, equivalently\, as the rank function for weak Bruhat order on the symmetric group. In this talk\, I’ll describe an analogous statistic on the reduced expressions for a given permutation that turns the Coxeter graph into a ranked poset with unique maximal element. This statistic simplifies greatly when shifting our paradigm from reduced expressions to balanced tableaux\, and I’ll use this simplification to give an elementary proof computing the diameter of the Coxeter graph for the long permutation. \nThis talk is elementary and assumes no background other than passing familiarity with the symmetric group.
URL:https://colleges.claremont.edu/ccms/event/tba-3/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20180911T121500
DTEND;TZID=America/Los_Angeles:20180911T131000
DTSTAMP:20180926T174358Z
CREATED:20180822T052223Z
LAST-MODIFIED:20180926T174358Z
UID:451-1536668100-1536671400@colleges.claremont.edu
SUMMARY:Small representations of integers by integral quadratic form (Lenny Fukshansky\, CMC)
DESCRIPTION:Given an isotropic integral quadratic form which assumes a value t\, we investigate the distribution of integer points at which this value is assumed. Building on the previous work about the distribution of small-height zeros of quadratic forms\, we produce bounds on height of points outside of some algebraic sets in a quadratic space at which the form assumes the value t. Our bounds on height are explicit in terms of heights of the form\, the space\, the algebraic set and the value t. Joint work with W. K. Chan. \nThe Fall 2018 organizational meeting for the ANTC seminar will be held at noon in the same room\, preceding the talk.
URL:https://colleges.claremont.edu/ccms/event/small-representations-of-integers-by-integral-quadratic-form/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
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