CMU Mathematics Department Colloquia

2019 -- 2020

Organizer

• Department of Mathematics Colloquium Coordinator C-Y. Jean Chan

• Because there might be a time delay in updating the webpage, please always check with the Coordinator for the available dates.

Meeting Times

Refreshments starts 30 minutes prior to the talk.
Typical Colloquium Talks are Thursday, 4:00–4:50pm, in Pearce 227. Refreshments are in Pearce 216.
There might be some talks scheduled on a different day and time, or in a different classroom. The following table gives the most accurate information for each event.

Schedule (in reversed chronological order)

Abstracts

Speaker: Siqi Fu (April 16)
Title: Canceled
Abstract: Event Canceled.

Speaker: Purnaprajna Bangere (April 9)
Title: TBD
Abstract: TBD

Speaker: Mark Iwen (March 19)
Title: Generalized Sparse Fourier Transforms for Approximating Functions of Many Variables
Abstract: Compressive sensing has generated tremendous amounts of interest since first being proposed by Emmanuel Candes, David Donoho, Terry Tao, and others a bit more than a decade ago. This mathematical framework has its origins in (i) the observation that traditional signal processing applications, such as MRI imaging problems, often deal with the acquisition of signals which are known a priori to be sparse in some basis, as well as (ii) the subsequent realization that this knowledge could in fact be used to help streamline the signal acquisition process in the first place (by taking the bare minimum of signal measurements necessary in order to discover and then reconstruct the important basis coefficients only). The resulting mathematical theory has since led to dramatic reductions in measurement needs over traditional approaches in many situations where one would previously have reconstructed a fuller set of a given signal's basis coefficients only to later discard most of them as insignificant.
Though extremely successful at reducing the number of measurements needed in order to reconstruct a given signal, most standard compressive sensing recovery algorithms still individually represent every basis function during the signal's numerical reconstruction. This leads one to ask a computationally oriented variant of the original question which led to the development of compressive sensing in the first place: why should one consider all possible basis coefficients individually during the numerical reconstruction of a given signal when one knows in advance that only a few of them will end up being significant? In fact, it turns out that one often does not have to explicitly consider each basis function individually during the reconstruction process, and so can reduce both the measurement needs *and* computational complexity of signal reconstruction to depend on the bare minimum of signal measurements necessary in order to reconstruct the important basis coefficients in many settings. This talk will discuss a class of sublinear-time numerical methods which do exactly this for functions that are sparse in the Fourier basis, as well as the extension of such techniques to produce new fast methods for approximating functions that are instead sparse in much more general bounded orthonormal system product bases.

Speaker: Special Film Screening (March 5)
Title: Secrets of The Surface - The Mathematical Vision of Maryam Mirzakhani
Abstract: This is a joint event of Mathematics Colloquium and Graduate Student Seminar sponsored by Department of Mathematics. The film features the first, and by far the only, woman mathematician Maryam Mirzakhani (1977-2017) who ever won the Fields Medal, the highest award in the field of mathematics, and often considered comparable to the Nobel Prize. The recipients must be under 40 years old. Mirzakhani was honored with the Fields Medal in the year 2014 for her research contributions in the world of Riemann Surfaces and Moduli Spaces. Following her dreams and passions since a teenage girl, to becoming a professor of Stanford University, Mirzakhani is an ideal role model for young women and minority individuals who wish to pursue a career in STEM areas. This event is free and open to the public.

Speaker: Melissa Liu (September 12)
Title: Counting Curves in a Quintic Threefold
Abstract: A quintic threefold is a degree 5 hypersurface in the 4-dimensional complex projective space. It is a compact Calabi-Yau threefold. In this talk, I will survey conjectures and results on counting curves in a smooth quintic threefold in the past three decades, including recent progress on counting higher genus curves.
Brief Bio: Melissa Liu received a Ph.D. degree in 2002 from Harvard University under the supervision of Shing-Tung Yao. Her research interests include Algebraic Geometry and Symplectic Geometry. Before joining Columbia University, she was a Junior Fellow at Harvard University and an Associate Professor at Northwestern University. Professor Liu won the Morningside Silver Medal in 2007 and was an invited ICM speaker in 2010. She is among the Inaugural Class of Fellows (2013) of the AMS.

Speaker: Kapil Paranjape (October 15)
Title: Beyond Abel and Jacobi
Abstract: The classical theorem of Abel and Jacobi characterises the zeroes and poles of a meromorphic function on a compact Riemann surface (or smooth projective variety) using a map which is nowadays called the Abel-Jacobi homomorphism.
Following the work of many algebraic geometers over the past 150 years, this result has been successively refined and studied for higher-dimensional varieties. The most sophisticated version of this refinement is via the theory of "motives" as first proposed by Grothendieck. The most elaborate conjectural refinements of the Abel-Jacobi theorem are those of Bloch and Beilinson.
As with most conjectures, there have been many attempts to construct counter-examples. One method is to construct "minimal" instances of these conjectures for "well-understood" varieties where the conjectures do not (as yet) follow from known results. Such examples were constructed by Griffiths, Mumford-Roitman and many others which led to the more precise formulations of the conjectures that we see today.
In this talk, the speaker will attempt to explain some ideas and examples behind this elaborate framework and present his own work in its context.

Speaker: Amy Shell-Gellasch (October 17, 18)
Title: Mathematical Devices at the Smithsonian: An Insider's View (October 17)
Abstract: As an historian of mathematics living in the Washington D.C. area from 2012-2017, Dr. Shell-Gellasch was an independent researcher at the Smithsonian's National Museum of American History. In that capacity she researched mathematical items held in the Smithsonian's collections and created the online content for those items on the museum's website. She also contributed to the museum's blog "Oh Say Can You See". In this talk Dr. Shell-Gellasch will share the research she did at the Smithsonian and highlight several of her favorite items and the mathematics behind them.
Workshop: Smithsonian Learning Lab: A Hands-on Workshop (October 18)
As an historian of mathematics living in the Washington D.C. area from 2012-2017, Dr. Shell-Gellasch was an independent researcher at the Smithsonian's National Museum of American History. In that capacity she researched mathematical items held in the Smithsonian's collections and created the online content for those items on the museum's website. She also contributed to the museum's blog "Oh Say Can You See". In this talk Dr. Shell-Gellasch will share the research she did at the Smithsonian and highlight several of her favorite items and the mathematics behind them.
Brief Bio: Dr. Amy Shell-Gellasch is a full time lecturer at Eastern Michigan University. She earned her DA in mathematics from the University of Illinois at Chicago in 2000 and followed that with a post doctorate position at the United States Military Institute at West Point. Her area of research is the History of Mathematics and its uses in teaching. She co-founded and currently chairs the History of Mathematics Special Interest Group of the MAA and is an associate editor of Convergence online journal. She conducted research on mathematical devices at the Smithsonian
National Museum of American History from 2012-2017, and continues to develop content and conduct training workshops for the Smithsonian's Digital Learning Lab, an online educational platform. Her article “The Spirograph and 19th Century German Mathematical Models” (Math Horizons, April, 2015) was included in <\b>Best Writing on Mathematics, 2016, Princeton University Press.

Speaker: Amit Savkar (November 7)
Title: Foundation to STEM Success: Placement, Adaptive Instruction, and Personalized Data Analytics
Abstract: It is not a surprise that students graduating from high school have big dreams to be part of the science, technology, engineering, and mathematics (STEM) ecosystem. It is also unsurprising that we as a country are not graduating nearly enough students to support the demands of STEM industries. The “M” in STEM is considered the hurdle keeping students from achieving their dream majors or from progressing smoothly through their chosen program. The talk will focus on a solution that has seen considerable success at UConn. It will focus on three main strategies, namely: i) Placement, ii) Adaptive Instruction, and iii) Personalized Analytics. I will provide you with the rationale, implementation, research methodologies, and results of adopting these three main strategies which reduced the DFW rates in our courses from pre-calculus through multivariable calculus.

Speaker: Ben Schmidt (December 5)
Title: Preserve One, Preserve All
Abstract: A 1953 theorem of Beckman and Quarles states that a self-map f of Euclidean n-space which satisfies d(f(x),f(y))=1 whenever d(x,y)=1 is an isometry. That is, for all pairs of points (x,y), there is equality d(x,y)=d(f(x),f(y)). I'll discuss a conjecture aiming to generalize this theorem in the realm of Riemannian geometry and some partial results. Based on joint work with Meera Mainkar.

Past Department Colloquia: Spring 2019 Fall 2018 Spring 2018 Fall 2017 Spring 2017 Fall 2016

Look for Colloquia Archives for past activities