Title: Spectral stability and spatial dynamics in partial differential equations
Abstract: Understanding the spectral stability of solutions to partial differential equations is an important step in predicting long-time dynamics. Recently, it has been shown that a topological invariant known as the Maslov Index can play an important role in determining spectral stability for systems that have a symplectic structure. Moreover, this perspective has lead to a framework for developing a spatial dynamics in multiple spatial dimensions. In this talk, the notions of spectral stability, the Maslov Index, and multidimensional spatial dynamics will be introduced and an overview of recent results will be given.
Abstract: Wallpapers are formed by repeating the same picture in a regular, periodic pattern. Have you ever wondered how many different wallpaper patterns are possible? Just a handful, or a very large number, or infinitely many? In this talk we will explore the answer to this question by considering the symmetries of wallpapers. Such symmetries make up the so-called crystallographic groups, and we will discuss their classification, as well as their connection to modern mathematics.
Biography: Dr. Pallavi Dani is an Associate Professor in the Department of Mathematics at Louisiana State University. She grew up in Mumbai, India and came to the United States to enter a doctoral program. She obtained her PhD from the University of Chicago in 2005. After brief postdocs at the University of Oklahoma and Emory University, she arrived at LSU in 2009. Her research has been funded by grants from the National Science Foundation and the Simons Foundation. In 2016 she was awarded the Ruth I. Michler Memorial Prize by the Association of Women in Mathematics in recognition of her research. Her work revolves around studying groups, which can be thought of as collections symmetries of spaces, from a geometric perspective.
This past year more than 4200 students at 570 institutions participated in the Putnam Mathematical Competition, with a median score of 2. Our Putnam team placed 21st nationally, and one of our team members ranked in the top 100 (Thomas Draper, placed 90.5 with a score of 51) and one other ranked in the top 200 (Daniel South, placed 168 with a score of 40).
Fifteen other participants received non-zero scores.
The William Lowell Putnam Mathematical Competition is the preeminent mathematics competition for undergraduate college students in the United States and Canada. The Putnam Competition takes place annually on the first Saturday of December. The competition consists of two 3-hour sessions, one in the morning and one in the afternoon. During each session, participants work individually on 6 challenging mathematical problems.
The Putnam began in 1938 as a competition between mathematics departments at colleges and universities. Now the competition has grown to be the leading university-level mathematics examination in the world. Although participants work independently on the problems, there is a team aspect to the competition as well. Institutions are ranked according to the sum of the scores of their three highest-scoring participants. Prizes are awarded to the participants with the highest scores and to the departments of mathematics of the five institutions the sum of whose top three scores is greatest.
The six mathematical problems in the competition are so challenging that the median score is often zero out of a possible 120 points. The competition is sponsored by the Mathematical Association of America.
NASA mathematician Katherine Coleman Goble Johnson, depicted in the movie “Hidden Figures” passed away this morning (Friday, February 24. 2020) at the age of 101. Johnson was a pioneer in space exploration; her work with NASA in mathematics led to the first American orbital spaceflight in 1962. Johnson ran all of the computer equations by hand for this flight, a remarkable feat that NASA administrator Jim Bridenstine stated, “helped our nation enlarge the frontiers of space even as she made huge strides that also opened doors for women and people of color.” Katherine Johnson was an incredible woman, an exceptional mathematician, and an American hero. For more information visit the following websites:
Abstract: Adding fractions feels like a cumbersome operation since we need to find a common denominator. What happens instead if we “add” fractions by simply adding their numerators and denominators? We’ll see that this leads to a beautiful construction called the Stern-Brocot tree that opens into a fertile mathematical landscape. Besides connections to important ideas in number theory, this tree has an intriguing application in the history of time-keeping.
Title: The L2 Theory of the Cauchy-Riemann Operator on Domains in Cn
Abstract: The Cauchy-Riemann operator governs the behavior of holomorphic functions, and the solvability of the Cauchy-Riemann equations is fundamentally different in one and several complex variables. In this talk, I will give an overview of the Cauchy-Riemann equation, its applications, and the current status of the problem.