Rutgers Graduate Student Analysis Seminar, Spring 2012

This is a general-audience seminar in mathematical analysis, aiming to provide an informal speaking environment for graduate students interested in analysis at large. Everyone is welcome to give a talk—even you, Mrs. Lovett, even I!—but we ask that each speaker keep the background to a minimum, preferably assuming no more than basic real and complex analysis covered in Math 501 and Math 503. If you are interested in giving a talk, please contact me or Katy—our contact information can be found below. If you are really interested in giving a talk, you might want to consider tips from senior mathematicians as to what constitutes a good talk: for example, here is Terence Tao’s advice. Please stay awhile and enjoy!

Location: Hill 525
Time: 4:50 – 5:50 on Mondays
Organizers: Katy Craig (katycc [at] math [dot] rutgers [dot] edu) and Mark Kim (markhkim [at] eden [dot] rutgers [dot] edu)

Upcoming Talks

Monday, February 20

Speaker: Moulik Kallupalam
Title: What’s Schrichartz Estimate?
Time: 4:50 – 5:50
Abstract: In the world where Fourier Transformed functions live, life is sweet, simple and fun. Going back and forth between this and our world, is often useful, and technical. We’ll talk a little about Fourier Transform, how it helps define spaces with fractional derivatives, and then talk about ” Strichartz estimates” for the wave equation in 3 space dimensions.

Monday, February 27

Speaker: Tom Sznigir
Title: TBA
Time: 4:50 – 5:50
Abstract: TBA

Monday, March 5

Speaker: Jianguo Xiao
Title: TBA
Time: 4:50 – 5:50
Abstract: TBA

Monday, March 19

Speaker: Xukai Yan
Title: TBA
Time: 4:50 – 5:50
Abstract: TBA

Monday, March 26

Speaker: Doug Schultz
Title: TBA
Time: 4:50 – 5:50
Abstract: TBA

Monday, April 2

Speaker: Liming Sun
Title: TBA
Time: 4:50 – 5:50
Abstract: TBA

Monday, April 9

Speaker: Bence Borda
Title: TBA
Time: 4:50 – 5:50
Abstract: TBA

Past Talks

Monday, January 30

Speaker: Mark Kim
Title: The Kakeya Problem in Harmonic Analysis
Time: 4:50 – 5:50
Abstract: What is the minimum area required to spin a needle around? Yes? Did you say, “That’s so 1920s”? Fear not! In this talk, we will present a bird’s-eye view of the problems known collectively as the Kakeya problem, ranging from theorems from 1970s to still-unsolved conjectures. The focus will be on the harmonic-analytic approach, though it should be noted that there are plenty of geometry, number theory, and combinatorics floating around in the scene. (notes)

Monday, February 6

Speaker: Katy Craig
Title: When an inf is also a sup: Fenchel-Rockafellar and Kantorovich duality
Time: 4:50 – 5:50
Abstract: Kantorovich duality says that the least amount of effort required to rearrange one pile of dirt to look like another is equal to the largest amount an enterprising friend could charge to perform the task for you (even with some constraints on his pricing structure). Thinking of probability measures as piles of dirt, the least amount of effort required to make one look like another provides a way to measure their distance, and Kantorovich duality tells you how to approximate this distance from above and below. I will reformulate the (discrete) Kantorovich problem as the minimization of a sum of two convex functions and prove Kantorovich duality as a consequence of Fenchel-Rockafellar. (notes)

Monday, February 13

Speaker: Po Lam Yung
Title: A “random theorem” in harmonic analysis
Time: 4:50 – 5:50
Abstract: In this talk, we will discuss a “random theorem” about randomness in harmonic analysis. The result dates back to Marcinkiewicz and Zygmund, and we will use this to prove Fefferman’s ball multiplier theorem. (notes)