The Algebraic Structures in Topology is a conference series that meets every two years in San Juan, Puerto Rico and is partially supported by the National Science Foundation , Purdue University , the Institute of the Mathematical Sciences of the Americas at the University of Miami , and the University of Puerto Rico at Rio Piedras. The conferences will feature a variety of events focusing on recent developments in algebraic topology and their applications to geometry, physics, and data science. The next iteration of the series will occur on June 5 – June 14, 2024. This event will have three…
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Congratulations to José Emilio Calderón Gómez for his successful Dissertation Defense. If the frame below does not scroll on your device click here.
Congratulations to Angélica M. Rosario Santos for her successful Dissertation Defense. If the frame below does not scroll on your device click here. This defense made history in our graduate program: Angélica M. Rosario Santos is the first Puerto Rican woman to obtain a Doctorate in Mathematics in Puerto Rico. Among others, the Dissertation Committee included doctors: Dr. María E. Pérez (UPRRP), Dr. Marta Álvarez (UPRRP) and Dr. Monica Alexander (U of Toronto).
Academic Class Schedule — August 2024 The class schedule is subject to changes. Below is the version of the schedule as of April 18, 2024. The document has several pages. If the frame below does not scroll on your device click here.
We consider the problem of finding curves of minimum time of descent, joining two given points over a given frictionless surface and under the influence of gravity. We discuss the existence and minimality of extremals for the corresponding time functional, and find explicit solutions in certain special cases, including a closed form solution for the problem on an inclined plane. A discussion of numerical methods for computing these minimizers is given with several numerical examples for which explicit solutions are not known. This paper is mostly expository. Our main contribution is to put together on a single reference different results…
Let V be a finite dimensional vector space over a field. The collection of all subspaces of V of a fixed dimension can be viewed as a geometric object in the sense that it is a nice projective algebraic variety, known as Grassmann variety. When the base field is finite with q elements, the Grassmann variety can be viewed as the “moduli space” of q-ary linear (error correcting) codes of a fixed length and dimension. Some questions about codes can be profitably studied from this viewpoint. More interestingly, the Grassmann variety itself leads to a special class of linear codes…
In the first part of the talk, some known results on the explicit distributions of integral functionals of Brownian motion will be shown, as well as some open problems related to them. In the second part, it will be shown how such functionals emerge in the finite-time blowup problem of systems of Stochastic Partial Differential Equations (SPDEs) and the open problems in this field of stochastic calculus.
The Department of Mathematics announces two Tenure Track positions, one in Discrete Mathematics and another in Numerical Analysis. Nevertheless, exceptional candidates in any area of Mathematics could also be considered. Position A Position B
Interior controllability properties of multi-d fractional pdes: what is the state of the art? We make a complete analysis of the interior controllability/orbservability properties of multi-D fractional partial differential equations. We show what is so far known and what is still unknown.