Math Department Seminar

Current: Spring 2024

■  January 24,  4 p.m. - 5 p.m. , UP 222

         Eric Weber, Iowa State University

          Title:  What is Data Science?

          Abstract:  Data science" is a buzzphrase making the rounds in academia and industry.  But is it more than  just a buzzphrase?  And if so, what exactly is it?  To turn the phrase: "Data science is in the eye of the beholder".  And what about machine learning and artificial intelligence?  We'll discuss my view of data science as well as several of my current research projects in the area.  We'll also talk about some of the mathematics behind data science as it currently stands.  Finally, I'll shamelessly promote the graduate program in Iowa State's mathematics department.

■  February 14,  4 p.m. - 5 p.m. , UP 222

        Daniel Perry, Augustana University

      Title:  The universal Lipschitz path space of the Heisenberg group 

      Abstract:  Inspired by the definition of a universal covering of a topological space, we define the universal Lipschitz path space over the Heisenberg group. The universal Lipschitz path space is a length space with a Lipschitz map onto the base space. As is the case with a universal cover of a topological space, the universal Lipschitz path space supports a unique lifting property and is Lipschitz simply connected. However, unlike the universal cover, no Lipschitz simply connected covering space of the Heisenberg group exists as the base space is nowhere Lipschitz semi-locally simply connected. These results follow from the Heisenberg group being a purely 2-unrectifiable metric space when endowed with the Carnot-Carathéordory metric. Further properties of the universal Lipschitz path space as well as applications to calculations of the Lipschitz fundamental group of the Heisenberg group will be discussed.

■      March 27, 4 p.m - 5 p. m., UP 222

        Soumodeep Mitra, University of South Dakota

      Title:  Probing the quantum nature of black holes with ultra-light boson environments

      Abstract: We show that the motion of a black hole (BH) through a cloud of an ultra-light scalar field, mimicking dark matter, is one of the best avenues to probe its quantum nature. This is because quantum effects can make the BH horizon reflective, with the largest reflectivity at smaller frequencies/smaller velocities, where the scattering of ultra-light scalar fields is most effective. In particular, we demonstrate that the quantum nature of BHs can lead to less energy flux, but larger frictional force experienced by them, resulting into an increase in the number of cycles in an extreme mass ratio inspiral. This provides a new window to probe the quantum nature of BHs, as well as ultra-light dark matter.