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 […]
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 […]
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 […]
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 […]
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 […]
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 […]
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 […]
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" […]
Title: What is the best shape? Geometric problems arising in aggregation models Abstract: How do pair interactions shape the large-scale behaviour of a cloud of particles (animals, social agents ...) […]
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 […]
The non-orientable 4-genus of a knot K is the smallest first Betti number of any non-orientable surface in the 4-ball spanning the knot. It is defined to be zero if the knot is slice. In joint work with Patrick Shanahan and Cornelia Van Cott, we attempt to determine the value of this invariant for double […]
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 […]
