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Voronoi Tessellations: Optimal Quantization and Modeling Collective Behavior (Prof. Rustum Choksi)

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Title: Voronoi Tessellations: Optimal Quantization and Modeling Collective Behavior Speaker: Prof. Rustum Choksi, Department of Mathematics and Statistics, McGill University Abstract:  Given a set of N distinct points (generators) in a domain (a bounded subset of Euclidean space or a compact Riemannian manifold), a Voronoi tessellation is a partition of the domain into N regions […]

Applied Math Seminar — Kathryn G. Link (UC Davis)

Emmy Noether Room, Estella 1021, Pomona College, 610 N. College Ave., Claremont, CA, United States

Title: Viscoelastic Effects of Spontaneous Oscillations of Elastic Filaments in the Follower-Force Problem. Abstract: It is well know that microorganisms, such as bacteria and eukaryotes, often move in intricate environments experiencing mechano-chemical dynamics. These environments consist of rheologically complex substances such as mucus and other biofilms that are more complicated than water.  Spermatozoa (sperm), for […]

Covering by polynomial planks (Alexey Glazyrin, University of Texas Rio Grande Valley)

On Zoom

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. We note that […]

Applied Math Seminar — Applied Attractions at Claremont Colleges

Emmy Noether Room, Estella 1021, Pomona College, 610 N. College Ave., Claremont, CA, United States

During this student-centered Applied Math Seminar, there will be discussion and presentation about upcoming courses in applied mathematics to help students make their enrollment choices for Fall 2022 and beyond.

Cusps in Convex Projective Geometry (Martin Bobb, IHES)

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Convex real projective structures generalize hyperbolic structures in a rich way. We will discuss a class of manifolds introduced by Cooper Long and Tillmann, which include finite-volume cusped hyperbolic manifolds and other manifolds with well-controlled ends. These manifolds have nice deformation theoretic properties, and we will conclude with an existence theorem for novel structures on […]

Geometry of continued fractions (Prof. Oleg Karpenkov)

Shanahan B460 (HMC) and Zoom - Hybrid

Title: Geometry of continued fractions Speaker:  Oleg Karpenkov, Department of Mathematical Sciences, University of Liverpool Abstract: In this talk we introduce a geometrical model of continued fractions and discuss its appearance in rather different research areas: -- values of quadratic forms (Perron Identity for Markov spectrum) -- the 2nd Kepler law on planetary motion -- Global relation […]

A conjugacy criterion for two pairs of 2 x 2 matrices over a commutative ring (Bogdan Petrenko, Eastern Illinois University)

On Zoom

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 2x2 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 […]

Linear independence, counting, and Hilbert’s syzygy theorem (Prof. Youngsu Kim)

Shanahan B460 (HMC) and Zoom - Hybrid

Title: Linear independence, counting, and Hilbert's syzygy theorem Speaker: Youngsu Kim, Department of Mathematics, Cal State San Bernardino Abstract: Linear independence is an essential concept in mathematics and one of the most fundamental notions in linear algebra. Linear algebra studies the solutions of linear equations. Algebraic geometry studies the solutions of polynomial equations (of arbitrary degree). […]

Applied Math Seminar — Alona Kryshchenko (CSUCI)

Emmy Noether Room, Estella 1021, Pomona College, 610 N. College Ave., Claremont, CA, United States

Title: Data science and applications in dynamic topic modeling Abstract: The shockwaves of the big data boom have thrown into sharp relief the critical need for domain-driven, large-scale data analytic techniques across the fields of, among others, finance, political science, economics, psychology, and medicine. It is not simply the size of data sets that contributes […]

Bounds for nonzero Littlewood-Richardson coefficients (Müge Taskin, Boğaziçi University, Turkey)

On Zoom

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 […]

Contact topology and geometry in high dimensions (Prof. Bahar Acu)

Shanahan B460 (HMC) and Zoom - Hybrid

Title: Contact topology and geometry in high dimensions Speaker: Bahar Acu, Department of Mathematics, Pitzer College Abstract: A very useful strategy in studying topological manifolds is to factor them into ``smaller" pieces. An open book decomposition of an n-manifold (the open book) is a special map (fibration) that helps us study our manifold in terms of its (n-1)-dimensional […]