### Week of April 14, 2019

 4:00pm to 5:00pm - RH 306 - Applied and Computational Mathematics Jiawang Nie - (UCSD) Symmetric Tensor Decompositions For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial.   A symmetric tensor decomposition can be determined by a set of generating polynomials, which can be represented by a generating matrix. Generally, a symmetric tensor decomposition can be determined by a generating matrix satisfying certain conditions. Based on them, an efficient method is given for computing symmetric tensor decompositions. 4:00pm to 6:00pm - MS 6221 - Geometry and Topology - (UCLA ) Joint LA Topology Seminar Talks at UCLA.  Please contact Li-Sheng Tseng if you plan to attend and would like to carpool.   Peter Lambert-Cole (Georgia Tech): Bridge trisections and the Thom conjecture The classical degree-genus formula computes the genus of a nonsingular algebraic curve in the complex projective plane. The well-known Thom conjecture posits that this is a lower bound on the genus of smoothly embedded, oriented and connected surface in CP2. The conjecture was first proved twenty-five years ago by Kronheimer and Mrowka, using Seiberg-Witten invariants. In this talk, we will describe a new proof of the conjecture that combines contact geometry with the novel theory of bridge trisections of knotted surfaces. Notably, the proof completely avoids any gauge theory or pseudoholomorphic curve techniques. James Conway (UC Berkeley): Classifying contact structures on hyperbolic 3-manifolds Two of the most basic questions in contact topology are which manifolds admit tight contact structures, and on those that do, can we classify such structures. In dimension 3, these questions have been answered for large classes of manifolds, but with a notable absence of hyperbolic manifolds. In this talk, we will see a new classification of contact structures on an family of hyperbolic 3-manifolds arising from Dehn surgery on the figure-eight knot, and see how it suggests some structural results about tight contact structures. This is joint work with Hyunki Min.
 4:00pm - RH 306 - Differential Geometry Nicos Kapouleas - (Brown University) The index and nullity of some Lawson surfaces  I will discuss some recent work with David Wiygul to determine the index and nullity of the Lawson surfaces desingularizing two orthogonal great two-spheres in the round three-sphere.
 12:00pm - RH 340N - Probability Preprint Seminar John Peca-Medlin - (UCI) Singularity of Bernoulli random matrices We will go over Tikhomirov’s argument on the asymptotic singularity of random Bernoulli matrices, found here: https://arxiv.org/pdf/1812.09016.pdf 3:00pm to 4:00pm - RH 306 - Number Theory Edray Goins - (Pomona College) ABC Triples in Families Given three positive, relative prime integers A, B, and C such that the first two sum to the third i.e. A + B = C, it is rare to have the product of the primes p dividing them to be smaller than each of the three.  In 1985, David Masser and Joseph Osterlé made this precise by defining a "quality" q(P) for such a triple of integers P = (A,B,C); their celebrated "ABC Conjecture" asserts that it is rare for this quality q(P) to be greater than 1 -- even through there are infinitely many examples where this happens.  In 1987, Gerhard Frey offered an approach to understanding this conjecture by introducing elliptic curves.  In this talk, we introduce families of triples so that the Frey curve has nontrivial torsion subgroup, and explain how certain triples with large quality appear in these families.  We also discuss how these families contain infinitely many examples where the quality q(P) is greater than 1.  This joint work with Alex Barrios. 4:00pm to 5:00pm - RH 306 - Colloquium Suzanne Sindi - (UC Merced) Mathematical Modeling of Prion Aggregate Dynamics within a Growing Yeast Population Prion proteins are responsible for a variety of neurodegenerative diseases in mammals such as Creutzfeldt-Jakob disease in humans and "mad-cow" disease in cattle. While these diseases are fatal to mammals, a host of harmless phenotypes have been associated with prion proteins in S. cerevisiae, making yeast an ideal model organism for prion diseases. Most mathematical approaches to modeling prion dynamics have focused on either the protein dynamics in isolation, absent from a changing cellular environment, or modeling prion dynamics in a population of cells by considering the "average" behavior. However, such models have been unable to recapitulate in vivo properties of yeast prion strains including experimentally observed rates of prion loss. My group develops physiologically relevant mathematical models by considering both the prion aggregates and their yeast host. We then validate our model and infer parameters through carefully designed in vivo experiments. In this talk, I will present two recent results. First, we adapt the nucleated polymerization model for aggregate dynamics to a stochastic context to consider a rate limiting event in the establishment of prion disease: the rst the successful amplication of an aggregate. We then develop a multi-scale aggregate and generation structured population model to study the amplication of prion aggregates in a growing population of cells. In both cases, we gain new insights into prion phenotypes in yeast and quantify how common experimentally observed outcomes depend on population heterogeneity.
 11:00am to 11:50am - PSCB 220 - Cryptography Travis Scholl - (University of California, Irvine) Smoothing Ideals in Quaternion Algebras In this talk we will go over one an algorithm of Kohel-Lauter-Petit-Tignol that, given a left ideal for a maximal order in a quaternion algebra, returns an equivalent left ideal with $\ell$-power reduced norm (The preprint can be found here: https://arxiv.org/pdf/1406.0981.pdf). This algorithm was mentioned in the previous talk as a supplementary algorithm to the reductions between certain computational problems. If there is time, we will also discuss a recent signatue scheme proposed by Galbraith-Petit-Silva based on this algorithm.