RIT on Applied Harmonic Analysis Archives for Fall 2022 to Spring 2023
Organization Meeting -- Applied Harmonic Analysis RIT
When: Wed, September 15, 2021 - 12:00pmWhere: Kirwan Hall 3206
Speaker: Radu Balan (UMD) -
Strichartz Estimates and the Quadratic Fourier Transform
When: Tue, September 21, 2021 - 12:30pmWhere: CSIC 4122
Speaker: Chris Dock (UMD) -
Strichartz Estimates and the Quadratic Fourier Transform (2)
When: Tue, September 28, 2021 - 12:30pmWhere: CSIC 4122 (CSCAMM)
Speaker: Chris Dock (UMD) -
Pure Localization Phenomena in Combinatorial Graph Laplacian Eigenvectors
When: Tue, October 5, 2021 - 12:30pmWhere: CSIC 4122 (CSCAMM Seminar Room)
Speaker: Shashank Sule (UMD) -
Abstract: Eigenvector Localization--the phenomenon where Graph Laplacian Eigenfunctions attain "small" values except for a neighborhood of the underlying domain--has gathered recent interest due to its applications in graph signal processing. In this talk we will discuss a slight variant of this phenomenon on Combinatorial Laplacians called Pure Localization, where an eigenfunction vanishes on a vertex and its neighborhood. We will review key definitions from spectral graph theory, and then go over some important examples of graphs which admit pure localization. We will also prove a gluing formula for purely localizing graphs. The last part of the talk will involve setting up the Neumann and Dirichlet theory of the Graph Laplacian, with the goal of proving that pure localization is equivalent to the existence of joint Dirichlet and Neumann eigenvectors. Using this equivalence, we will derive some simple necessary conditions for purely localizing graphs.
Pure Localization Phenomena in Combinatorial Graph Laplacian Eigenvectors (2)
When: Tue, October 12, 2021 - 12:30pmWhere: CSIC 4122
Speaker: Shashank Sule (UMD) -
Abstract: Eigenvector Localization--the phenomenon where Graph Laplacian Eigenfunctions attain "small" values except for a neighborhood of the underlying domain--has gathered recent interest due to its applications in graph signal processing. In this talk we will discuss a slight variant of this phenomenon on Combinatorial Laplacians called Pure Localization, where an eigenfunction vanishes on a vertex and its neighborhood. We will review key definitions from spectral graph theory, and then go over some important examples of graphs which admit pure localization. We will also prove a gluing formula for purely localizing graphs. The last part of the talk will involve setting up the Neumann and Dirichlet theory of the Graph Laplacian, with the goal of proving that pure localization is equivalent to the existence of joint Dirichlet and Neumann eigenvectors. Using this equivalence, we will derive some simple necessary conditions for purely localizing graphs.
Permutation invariant embeddings
When: Tue, October 19, 2021 - 12:30pmWhere: CSIC 4122
Speaker: Stratos Tsoukanis (UMD) -
Abstract: The goal of the talk is to describe a bi-Lipshitz embedding of the quotient space of matrices modulo row permutation and of quotient space of symmetric square matrices modulo row and column permutation.
In the talk we will see an example of a bi-Lipshitz embedding b_A created by sorting after multiplying a key matrix A.
For a fixed matrix A, the set of matrices X, such that b_A(X)= b_A(Y) iff Y is a row permutation of Y are called the
separation set of A. We will talk about properties of separated sets, and then explain under what conditions the
map b_A is an Bi-Lipschitz injection of this quotient space.
Permutation invariant embeddings
When: Tue, October 26, 2021 - 12:30pmWhere: CSIC 4122
Speaker: Stratos Tsoukanis (UMD) -
Recent advances in bandit learning analysis
When: Tue, November 2, 2021 - 12:30pmWhere: CSIC 4122
Speaker: Michael Rawson (UMD) -
Abstract: A look at reinforcement learning via bandit learning. We'll introduce the problem and solutions. We'll look at recent advances and performance metrics. Finally, we'll talk about future directions.
Assignment Problems: From Linear to Hypergraphical Point-set Matching
When: Tue, November 9, 2021 - 12:30pmWhere: CSIC 4122
Speaker: Andrew Lauziere (UMD) -
Abstract: Assignment problems describe the mathematical task of matching objects between sets. The combinatorial optimization problems depend upon rigid constraints under an an objective function detailing relationships between objects across sets. The progression in objective complexity is explored with examples of applications. The simplest linear assignment problem has a polynomial time solution. However, moderately more intricate objective functions are NP-hard, requiring heuristic algorithms to return approximate solutions. The most complex of assignment problems can be modeled via hypergraphs, and solved optimally via a proposed branch-and-bound algorithm.
A Schatten Class Result for Fourier Integral Operators
When: Tue, November 16, 2021 - 12:30pmWhere: CSIC 4122
Speaker: Canran Polo Ji (UMD) -
Abstract: We discuss operators of the form:
Af(x)=\int\int b(x,y,\xi)f(y)exp[2pi*i\psi(x,y,\xi)] dyd\xi,
where b is a symbol and \psi is a phase function.
The main result reads as follows. Assume A is a linear operator on L^2(R^d) of the form above, where p \in [1,2], and c is a second class Fourier integral operator slice permutation. For certain values of p_1,...,p_6d, If the kernel of A, b*exp[2pi*i\psi(x,y,\xi)] \in M(c)^{p_1,...,p_6d}, the mixed modulation space, then A belongs to the Schatten p-class.
The proof of this theorem is based on Shannon Bishop’s PhD thesis and one corollary of that thesis.
A Schatten Class Result for Fourier Integral Operators (II)
When: Tue, November 23, 2021 - 12:30pmWhere: CSIC 4122
Speaker: Canran Polo Ji (UMD) -
Abstract: We discuss operators of the form:
Af(x)=\int\int b(x,y,\xi)f(y)exp[2pi*i\psi(x,y,\xi)] dyd\xi, where b is a symbol and \psi is a phase function.
The main result reads as follows. Assume A is a linear operator on L^2(R^d) of the form above, where p \in [1,2], and c is a second class Fourier integral operator slice permutation. For certain values of p_1,...,p_6d, If the kernel of A, b*exp[2pi*i\psi(x,y,\xi)] \in M(c)^{p_1,...,p_6d}, the mixed modulation space, then A belongs to the Schatten p-class.
The proof of this theorem is based on Shannon Bishop’s PhD thesis and one corollary of that thesis.
CUR Algorithms
When: Tue, November 30, 2021 - 12:30pmWhere: CSIC 4122
Speaker: Kathryn Linehan (UMD) -
Abstract: We will discuss multiple CUR algorithms. The focus will be on the algorithms and how they perform in practice. Algorithms include deterministic and randomized methods and will be presented in chronological order. Applications may also be presented.
CUR Algorithms (2)
When: Tue, December 7, 2021 - 12:30pmWhere: CSIC 4122
Speaker: Kathryn Linehan (UMD) -
Abstract: We will discuss multiple CUR algorithms. The focus will be on the algorithms and how they perform in practice. Algorithms include deterministic and randomized methods and will be presented in chronological order. Applications may also be presented.