Vertical Integration Workshop, April 16-19





We had so much fun when ran this workshop in October, we decided to do it again! This time, we are going to have faculty, postdocs, graduate students and undergraduates listening to each other's talks and interacting throughout. The talks are labeled (F) for faculty, (P) for postdoc, (G) for gradstudent, and (U) for undergrad. The abstracts can be found at the bottom of this page.


Thursday, April 16 (Hylan 1106A)

3.30 p.m. Sarah Tammen (P), University of Wisconsin (this talk will double as as the Combinatorics Seminar lecture)
Title: Incidence estimates for tubes

4.30 p.m. Question and answer session with Sarah Tammen about her talk and her work.


Friday, April 17 (Dewey 2110E)

9.00 a.m. Camil Muscalu (F), Cornell University (this talk will double as a Analysis Seminar lecture)
Title: On a Brascamp-Lieb type theory for singular integrals

10.00 a.m. Question and answer session with Camil Muscalu about his talk and his work.

10.30 a.m. Will Burstein (G), University of Rochester
Title: The Fourier ratio as the unifying complexity parameter

11.00 a.m. Lunch break

12.45 p.m. Eyvindur Palsson (F), Virginia Tech University (this talk will double as an Analysis Seminar lecture)
Title: Falconer type results for distance graphs

1.45 p.m. Question and answer session with Eyvi Palsson about his talk and his work.

2.15 p.m. Quy Pham (G), University of Rochester
Title: Projection theory, Fourier Integral Operators, and point configurations

2.45 p.m. Hari Nathan (G),  University of Rochester
Title: On a fractal variant of Principal Component Analysis

3.15 p.m. Chamsol Park (P), University of Rochester

4.15 p.m. Question and answer session with Chamsol Park about his talk and his work.


Saturday, April 18 (Hylan 1106A)

8.00 a.m. Neeraja Kulkarni (P), University of Rochester

9.00 a.m. Question and answer session with Neeraja Kulkarni about her talk and her work.

9.30 a.m. Shengze Duan (G), University of Rochester
Title: Signal recovery and restriction theory in the Euclidean setting

10.00 a.m. Zhangze Li (G), Ohio State University

10.30 a.m. Nate Shaffer (U), University of Rochester

11.00 a.m. Steven Senger (F), University of Missouri

12.00 p.m. Question and answer session with Steven Senger about his talk and his work.

12.30 p.m.- 1.30 p.m. Lunch

1.30 p.m. Masha Gordina (F), University of Rochester

2.30 p.m. Question and answer session with Masha Gordina about her talk and her work.

3.00 p.m. Zhihe Li (G), University of Rochester
Title: Fourier Ratio in the Euclidean setting

3.30 p.m. Ella Yu (G), University of Rochester
Title: Generalized Salem sets and Bourgain's inequality

4.00 p.m. James Roan (G), University of Rochester

4.30 p.m. Krystal Taylor (F), Ohio State University (zoom talk)
Title: Nonlinear Projections and Quantitative Rectifiability

5.30 p.m. Question and answer session with Krystal Taylor about her talk and her work.

6.00 p.m. Pizza Party!!!


Sunday, April 19 (Hylan 1106A)

8.00 a.m. Vishal Gupta (P), University of Rochester
Title: A lower bound on the smallest eigenvalue of a graph and its application to the associahedron graph

9.00 a.m. Question and answer session with Vishal Gupta about his talk and his work.

9.30 a.m. Nathaniel Kingsbury-Neuschotz (G), University of Rochester
Title: Strong approximation for the character variety of the four-times punctured sphere

10.00 a.m. Shantanu Deodhar (G), University of Rochester
Title: Spectral synthesis with the complexity parameter

10.30 a.m. Emmett Wyman (F), SUNY Binghamton
Title: Spectral synthesis on Riemannian manifolds

11.30 Question and answer session with Emmett Wyman about his talk and his work.


Abstracts:

Sarah Tammen: I will discuss incidence estimates for slabs which are formed by intersecting small neighborhoods of well-spaced hyperplanes in R^d with the unit cube [0,1]^d. My work is an analogue of a theorem of Guth, Solomon, and Wang, who proved a version of the Szemerédi- Trotter theorem for thin tubes that satisfy a certain strong spacing condition. My proof uses induction on scales and the high-low method of Vinh, along with geometric insights.

Camil Muscalu: The plan of the lecture is to describe some examples of natural estimates for singular integrals, that are analogous to the classical Brascamp-Lieb inequality. Joint work with Cristina Benea.

Will Burstein:

Eyvi Palsson: The Falconer distance problem, a major open problem on the interface of geometric measure theory and harmonic analysis, has seen much progress in the last decade. There are many variants of it, including pinned and non-empty interior ones, as well as multi-point configuration analogues. In this talk I will give a brief introduction and report on some recent results on general distance graph variants of this classic question.

Quy Pham:

Hari Nathan:

Chamsol Park:

Neeraja Kulkarni:

Shengze Duan:

Zhangze Li:

Nate Shaffer:

Steve Senger:

Masha Gordina:

Zhihe Li:

Ella Yu:

James Roan:

Krystal Taylor: From the delicate geometry found in a snowflake to the intricate patterns of a coastal shoreline, nature holds infinite patterns and scales.  The world is not easily described using mere lines and cones, and classic Euclidean geometry falls short.  The notion of fractals gives us a language and a set of tools to understand more complex phenomena. 

Vishal Gupta:

Nathaniel Kingsbury-Neuschotz:

Shantanu Deodhar:

Emmett Wyman: