Graduate Program

Spring Term Schedule

Spring 2025

Number	Title	Instructor	Time
MATH 403-1 Theory of Probability Arjun Krishnan TR 9:40AM - 10:55AM
Prerequisites: MATH 471 Description: Measure-theoretic foundations of probability. The Radon-Nikodym theorem and conditional expectation. Infinite products and Kolmogorov's extension theorem. Random variables, modes of convergence, independence, and the monotone class theorem. Laws of large numbers. Characteristic functions and the central limit theorem. Martingales, Doob's and Kolmogorov's inequalities, the optional sampling theorem. Introduction to stochastic processes. Location (TR 9:40AM - 10:55AM)
MATH 437-1 Algebra II Naomi Jochnowitz MW 4:50PM - 6:05PM
Prerequisites: MATH 436. Permission of instructor required for undergraduates. Description:Multilinear algebra, quadratic forms, simple and semi-simple rings and modules. Location (MW 4:50PM - 6:05PM)
MATH 448-01 Computational Topology Jonathan Pakianathan MW 12:30PM - 1:45PM
Prerequisites: Linear algebra (165/173 or equivalent), multivariable calculus (164/174 or equivalent) and either some real analysis or topology (265 or 240 or equivalent). Computational topology is an emerging field of study at the intersection of mathematics and computer science which is devoted to the study of efficient algorithms for topological problems, especially those that arise in other areas of computing. Possible topics include: algorithms involving polygons, polyhedra and their triangulations, Voronoi cells and convex hull construction with applications, algorithms for simplicial complexes and their homology, persistent homology of large data sets (topological data analysis), discrete Morse theory, discrete differential geometry, and normal surface theory. Computing topics may include algorithms for computing topological invariants, ranking alternatives with incomplete data (netflix problem), curve and surface reconstruction, robotic motion planning, sensor array construction and methods for detecting topological patterns in large data sets beyond traditional cluster analysis or manifold fitting. Location (MW 12:30PM - 1:45PM)
MATH 453-1 Differentiable Manifolds Stephen Kleene TR 2:00PM - 3:15PM
Prerequisites: MATH 255 and 265. Permission of instructor required for undergraduates. Description: Differentiable manifolds, mappings and embeddings, exterior differential forms, affine connections, curvature and torsion. Riemannian geometry, introduction to Lie groups and Lie algebras. Location (TR 2:00PM - 3:15PM)
MATH 467-1 Analysis II Dinesh Thakur MW 10:25AM - 11:40AM
Prerequisites: Math 471. Description: analytic functions as mappings, complex integration, series and product developments, conformal mapping and Dirichlet’s problem, Hilbert spaces, Fourier transform and Sobolev spaces. Location (MW 10:25AM - 11:40AM)
MATH 506-1 Topics in Probability Sevak Mkrtchyan MW 10:25AM - 11:40AM
The course will explore applications of algebraic methods to studying probabilistic models. We will discuss symmetric functions. Schur and Macdonald polynomials and their applications to the lozenge tiling, directed polymer and other models Location (MW 10:25AM - 11:40AM)
MATH 533-01 Algebraic Curves Dinesh Thakur MW 12:30PM - 1:45PM
“An introduction to algebraic curves and applications in the global, local and finite field cases.” Location (MW 12:30PM - 1:45PM)
MATH 565-1 Partial Differential Equation Xuwen Chen TR 9:40AM - 10:55AM
Linear partial differential operators with constant coefficients. Elementary solutions; elliptic, hypo-elliptic, and hyperbolic operators. Location (TR 9:40AM - 10:55AM)
MATH 578-01 Topics in Harmonic Analysis Alex Iosevich M 6:15PM - 8:45PM
The central theme of the course is decoupling. This technique has been used extensively in recent years in harmonic analysis and number theory. The proof of the celebrated Vingoradov conjecture by Bourgain and Demeter, significantly improved exponents for the Falconer distance problems by Guth, Iosevich, Ou, and Wang in , and tremendous progress in the study of the moments of the Riemann zeta function by Bourgain and Watt, among many other results, has been accomplished using decoupling. We will also go over the background materials in harmonic analysis, including restriction theory and related topics. Location (M 6:15PM - 8:45PM)
MATH 591-01 PhD Readings in Math Alex Iosevich 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 591-02 PhD Readings in Math Sevak Mkrtchyan 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 591-03 PhD Readings in Math Naomi Jochnowitz 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 591-04 PhD Readings in Math Thomas Tucker 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 591-05 PhD Readings in Math Stephen Kleene 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 591-06 PhD Readings in Math Jonathan Pakianathan 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 591-07 PhD Readings in Math Dinesh Thakur 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 591-08 PhD Readings in Math Douglas Ravenel 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 591-09 PhD Readings in Math Steven Gonek 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 591-10 PhD Readings in Math Xuwen Chen 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 591-11 PhD Readings in Math Sema Salur 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 591-12 PhD Readings in Math Dan Geba 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 591-13 PhD Readings in Math Juan Rivera Letelier 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 591-14 PhD Readings in Math Arjun Krishnan 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 591-15 PhD Readings in Math Carl Mueller 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 591-22 PhD Readings in Math Allan Greenleaf 7:00PM - 7:00PM
No description Location ( 7:00PM - 7:00PM)
MATH 595-01 PhD Research in Math Juan Rivera Letelier 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 595-02 PhD Research in Math Jonathan Pakianathan 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 595-03 PhD Research in Math Douglas Ravenel 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 595-04 PhD Research in Math Alex Iosevich 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 595-05 PhD Research in Math Carl Mueller 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 595-06 PhD Research in Math Thomas Tucker 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 595-07 PhD Research in Math Allan Greenleaf 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 595-08 PhD Research in Math Dinesh Thakur 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 595-09 PhD Research in Math Stephen Kleene 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 595-10 PhD Research in Math Steven Gonek 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 595-11 PhD Research in Math Xuwen Chen 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 595-12 PhD Research in Math Dan Geba 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 595-13 PhD Research in Math Sema Salur 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 595-14 PhD Research in Math Naomi Jochnowitz 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 595-15 PhD Research in Math Arjun Krishnan 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 595-16 PhD Research in Math Sevak Mkrtchyan 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 895-1 Cont of Master's Enrollment – 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 897-1 Master's Dissertation Naomi Jochnowitz 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 899-1 Master's Dissertation Naomi Jochnowitz 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 995-1 Cont of Doctoral Enrollment Sevak Mkrtchyan 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)
MATH 999-01 Doctoral Dissertation Sevak Mkrtchyan 7:00PM - 7:00PM
Blank Description Location ( 7:00PM - 7:00PM)

Number	Title	Instructor	Time
Monday
MATH 578-01 Topics in Harmonic Analysis Alex Iosevich
The central theme of the course is decoupling. This technique has been used extensively in recent years in harmonic analysis and number theory. The proof of the celebrated Vingoradov conjecture by Bourgain and Demeter, significantly improved exponents for the Falconer distance problems by Guth, Iosevich, Ou, and Wang in , and tremendous progress in the study of the moments of the Riemann zeta function by Bourgain and Watt, among many other results, has been accomplished using decoupling. We will also go over the background materials in harmonic analysis, including restriction theory and related topics.
Monday and Wednesday
MATH 467-1 Analysis II Dinesh Thakur
Prerequisites: Math 471. Description: analytic functions as mappings, complex integration, series and product developments, conformal mapping and Dirichlet’s problem, Hilbert spaces, Fourier transform and Sobolev spaces.
MATH 506-1 Topics in Probability Sevak Mkrtchyan
The course will explore applications of algebraic methods to studying probabilistic models. We will discuss symmetric functions. Schur and Macdonald polynomials and their applications to the lozenge tiling, directed polymer and other models
MATH 448-01 Computational Topology Jonathan Pakianathan
Prerequisites: Linear algebra (165/173 or equivalent), multivariable calculus (164/174 or equivalent) and either some real analysis or topology (265 or 240 or equivalent). Computational topology is an emerging field of study at the intersection of mathematics and computer science which is devoted to the study of efficient algorithms for topological problems, especially those that arise in other areas of computing. Possible topics include: algorithms involving polygons, polyhedra and their triangulations, Voronoi cells and convex hull construction with applications, algorithms for simplicial complexes and their homology, persistent homology of large data sets (topological data analysis), discrete Morse theory, discrete differential geometry, and normal surface theory. Computing topics may include algorithms for computing topological invariants, ranking alternatives with incomplete data (netflix problem), curve and surface reconstruction, robotic motion planning, sensor array construction and methods for detecting topological patterns in large data sets beyond traditional cluster analysis or manifold fitting.
MATH 533-01 Algebraic Curves Dinesh Thakur
“An introduction to algebraic curves and applications in the global, local and finite field cases.”
MATH 437-1 Algebra II Naomi Jochnowitz
Prerequisites: MATH 436. Permission of instructor required for undergraduates. Description:Multilinear algebra, quadratic forms, simple and semi-simple rings and modules.
Tuesday
Tuesday and Thursday
MATH 403-1 Theory of Probability Arjun Krishnan
Prerequisites: MATH 471 Description: Measure-theoretic foundations of probability. The Radon-Nikodym theorem and conditional expectation. Infinite products and Kolmogorov's extension theorem. Random variables, modes of convergence, independence, and the monotone class theorem. Laws of large numbers. Characteristic functions and the central limit theorem. Martingales, Doob's and Kolmogorov's inequalities, the optional sampling theorem. Introduction to stochastic processes.
MATH 565-1 Partial Differential Equation Xuwen Chen
Linear partial differential operators with constant coefficients. Elementary solutions; elliptic, hypo-elliptic, and hyperbolic operators.
MATH 453-1 Differentiable Manifolds Stephen Kleene
Prerequisites: MATH 255 and 265. Permission of instructor required for undergraduates. Description: Differentiable manifolds, mappings and embeddings, exterior differential forms, affine connections, curvature and torsion. Riemannian geometry, introduction to Lie groups and Lie algebras.
Wednesday
Thursday
Friday