feldman (at) math.utah.edu),
Victoria Kala (victoria.kala (at) utah.edu),
or Akil Narayan (akil (at) sci.utah.edu)Monday, February 10 at 4pm. In-person LCB 222
Speaker: Leonid Kunyansky
Department of Mathematics, University of Arizona
Title: Hybrid imaging modalities and the range of the spherical means transform
Abstract: The last two decades saw proliferation of novel coupled-physics imaging
modalities. A variety of sensitive but safe and inexpensive medical imaging
methods has been developed, that hold great promise for the breast imaging for
cancer, detection of ischemia, hemorrhaging, blood clots, etc. These imaging
techniques work by combining high-resolution ultrasound with electromagnetic
fields that are highly sensitive to the features of interest. In the first
part of my talk I will overview the most interesting of these modalities, with
emphasis on the underlying mathematics.
Inevitably, the introduction of the new techniques has posed a variety of new
and exciting inverse problems. In particular, a prominent role in this field is
played by the spherical means operator, that maps a function into a collection
of integrals over spheres with centers lying on a given surface. The problem
I will discuss is the description of the range of this operator. As it
happens, all of the classical results are suboptimal, in that they use twice
the amount of needed data. I will present a novel range description, that
overcomes this issue.
(This is a joint work with Peter Kuchment, Texas A&M University)
Monday, February 24 at 10am. In-person JTB 110 (Joint seminar with SIAM Northern States Section)
Speaker: Gautam Iyer
Department of Mathematical Sciences, Carnegie Mellon University
Title: Enhanced Dissipation and Mixing
Abstract: Consider a drop of dye in water. If left alone it takes a very
long time to mix. If you stir it a little, it mixes quickly. This is due
to a enhanced dissipation, a phenomenon where the combined effect
of convection and diffusion increase the rate of energy dissipation.
This effect can be analyzed mathematically by using PDE methods to study
the advection diffusion equation, or using probabilistic methods to
study the mixing time of the associated Itô diffusion. This talk will be
an overview several recent results in this field, and present the main
ideas from both PDE and probabilistic perspectives.
Monday, February 24 at 4pm. In-person LCB 222
Speaker: Robyn Brooks
Science Research Initiative, University of Utah
Title: Computing Invariants of Multi Parameter Persistence Modules
Abstract: Persistent Homology is a tool of Computation Topology which is used to determine the topological features of a space from a sample of data points. In this talk, I will introduce the persistence pipeline and some cool applications of persistent homology. I will then present some basic tools from Discrete Morse Theory which can be used to better understand the multi-parameter persistence module of a filtration. In particular, the addition of a discrete gradient vector field consistent with a multi-filtration allows one to exploit the information contained in the critical cells of that vector field as a means of enhancing geometrical understanding of multi-parameter persistence. Results from joint work with Claudia Landi, Asilata Bapat, Barbara Mahler, and CeliaHacker, show that the rank invariant for nD persistence modules can be computed by selecting a small number of values in the parameter space determined by the critical cells of the discrete gradient vector field. These values may be used to reconstruct the rank invariant for all other possible values in the parameter space. I will then present some of my current research in other related invariants for multi-parameter persistence modules.
Monday, March 3 at 4pm. In-person LCB 222
Speaker: Kevin Miller
Department of Mathematics, Brigham Young University
Title: TBD
Abstract: TBD
Monday, March 17 at 4pm. In-person LCB 222
Speaker: Jesse Chan
Department of Computational Applied Mathematics and Operations Research, Rice University
Title: TBD
Abstract: TBD
Monday, March 24 at 4pm. In-person LCB 222
Speaker: Pascal Steinke
Institute for Applied Mathematics, University of Bonn
Title: TBD
Abstract: TBD
Monday, 31 at 10am. In-person JTB 110 (Joint seminar with SIAM Northern States Section)
Speaker: Katie Newhall
Department of Mathematics, UNC Chapel Hill
Title: TBD
Abstract: TBD
April 7 at 10am. In-person JTB 110 (Joint seminar with SIAM Northern States Section)
Speaker: Svetlana Tokareva
Los Alamos National Laboratory
Title: TBD
Abstract: TBD
April 14 at 10am. In-person JTB 110 (Joint seminar with SIAM Northern States Section)
Speaker: Lia Bronsard
Department of Mathematics and Statistics, McMaster University
Title: TBD
Abstract: TBD
April 14 at 4pm. In-person LCB 222
Speaker: Mike Novack
Department of Mathematics, Louisiana State University
Title: TBD
Abstract: TBD
feldman (at) math.utah.edu),
Victoria Kala (victoria.kala (at) utah.edu),
and
Akil Narayan (akil (at) sci.utah.edu).
Past lectures: Fall 2024, Spring 2024, Fall 2023, Spring 2023, Fall 2022, Spring 2022, Fall 2021, Spring 2021, Fall 2020, Spring 2020, Fall 2019, Spring 2019, Fall 2018, Spring 2018, Fall 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006, Spring 2006, Fall 2005, Spring 2005, Fall 2004, Spring 2004, Fall 2003, Spring 2003, Fall 2002, Spring 2002, Fall 2001, Spring 2001, Fall 2000, Spring 2000, Fall 1999, Spring 1999, Fall 1998, Spring 1998, Winter 1998, Fall 1997, Spring 1997, Winter 1997, Fall 1996, Spring 1996, Winter 1996, Fall 1995.