Graduate Program

Term Schedule

Fall 2020

Number	Title	Instructor	Time
MATH 436-1 Algebra I Naomi Jochnowitz MW 4:50PM - 6:05PM
Prerequisites: MTH 237 or equivalent. Undergrads must have permission of Instructor. Description: Rings and modules, group theory, fields and Galois theory. Location (MW 4:50PM - 6:05PM)
MATH 440-1 General Topology Jonathan Pakianathan MW 12:30PM - 1:45PM
Prerequisites: MTH 265 or equivalent. Permission of instructor required for Undergraduates. Description: The first half of the course will study the general topological notions of topological space, metric spaces, quotient spaces, connectedness, compactness, manifolds and topological groups. The second half of the course will be an introduction to the differential topology of smooth manifolds. Topics include Sard’s theorem, transversality, intersection theory and applications such as the Jordan-Brouwer separation theorem, the Borsuk-Ulam theorem and the Poincare-Hopf theorem. This course will not cover the theory of differential forms, distributions or integration on manifolds which is usually covered in our spring graduate differentiable manifolds course instead. Location Gavett Hall Room 206 (MW 12:30PM - 1:45PM)
MATH 443-1 Algebraic Topology Douglas Ravenel MW 2:00PM - 3:15PM
Prerequisites: MTH 436 and MTH 440. Permission of instructor required for Undergraduates. Description: The combinatorial structure of complexes and the homology of polyhedra; applications of algebraic techniques in topology to classification of surfaces, fixed point theory, and analysis. Location (MW 2:00PM - 3:15PM)
MATH 471-1 Real Analysis Dan Geba TR 9:40AM - 10:55AM
Prerequisites: MTH 265 or equivalent. Description: Lebesgue measure on the line; measure spaces; integration; convergence theorems; Radon-Nikodym theorem; differentiation; Fubini's theorem; function spaces. Location Hylan Building Room 202 (TR 9:40AM - 10:55AM)
MATH 472-1 Functional Analysis Allan Greenleaf MW 10:25AM - 11:40AM
Banach spaces; dual spaces; Riesz representation theorem; Hilbert spaces; Fourier series; projective and unitary operators; spectral analysis of completely continuous self-adjoint operators. Applications. Location (MW 10:25AM - 11:40AM)
MATH 483-1 2nd Year Grad Orientation Alex Iosevich –
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MATH 492-1 Grad Professional Seminar Doug Haessig –
Prerequisites: Open to first-year graduate students only. Description: This course is a requirement for math Ph.D. students during their first fall in the Ph.D. program. The course will advise them on various aspects of their professional development. It will address:a) Research practices and development: Creating a CV, creating a professional webpage, milestones for grad school, grants and funding, conferences.b) Teaching: Responsibilities, techniques, etc.c) Community: Attendance of colloquia, seminars, meeting with faculty, etc.d) Other: Discussion of arXiv, math-sci net, latex, peer support network, etc.
MATH 493-1 Current Topics in Math – –
Prerequisites: Open to second year graduate students only. Description: Students will attend a selection of research talks and colloquia on current research in Mathematics. Required of math Ph.D. students during their 2nd fall in the Ph.D. program
MATH 506-1 Advanced Topics in Probability Theory Carl Mueller MW 3:25PM - 4:40PM
Topics are related to recent research in the field. Location (MW 3:25PM - 4:40PM)
MATH 507-1 Advanced Topics in Probability: First and Last Passage Percolation Arjun Krishnan TR 9:40AM - 10:55AM
First-Passage Percolation (FPP) is a simple shortest path problem on a graph: pick a graph; put some random weights on its edges to mimic the time to cross edges; pick any two vertices and _nd the shortest time (weight) path between them. The passage time between vertices is a random metric on the graph, and the shortest-time paths are geodesics for this metric. One usually studies the statistics of the passage time and the behavior of geodesics on Zd. This simple model has incredible connections to 1) the zeros of the zeta function 2) random matrix theory 3) representation theory and combinatorics 4) Hamilton-Jacobi PDEs. The model was proposed in the 60s, but the main questions in the _eld are almost entirely open. In this course, I will loosely follow the review \50 years of _rst-passage percolation", and then move on to the research level questions in towards the end of the course. Along the way, I intend to cover: (1) Shortest path and ow algorithms, (2) Geodesic dynamics through ergodic theory, and (3) Hamilton-Jacobi PDEs and nonlinear eigenvalue problems. The course will be mostly probabilistic and analytic. The prerequisites are the basic real analysis and probability courses: 471 and 406. However, I think you can easily manage if you've only taken one of these. Location (TR 9:40AM - 10:55AM)
MATH 531-1 Algebraic Num Theory Naomi Jochnowitz MW 2:00PM - 3:15PM
Valuations, ideal theory, divisors. Class number, unit theorem. Geometric applications. Location (MW 2:00PM - 3:15PM)
MATH 549-1 Toric Topology Frederick Cohen MWF 11:50AM - 12:40PM
The main direction of this subject is a development of topological spaces known as moment-angle complexes as well as toric manifolds. Moment-angle complexes are unions of products of circles, and 2-disks"indexed" by a finite simplicial complex. Moment-angle complexes admit actions of products of circles with orbit spaces frequently known as toric manifolds. These spaces and their properties are at the interface of topology, geometry, algebraic topology as well as combinatorics. The goal of the course is to develop some of the main structure theorems in the subject. There will be a strong emphasis on examples which will be developed in class. Location (MWF 11:50AM - 12:40PM)
MATH 591-01 PhD Readings in Math Frederick Cohen –
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MATH 591-02 PhD Readings in Math Allan Greenleaf –
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MATH 591-03 PhD Readings in Math Alex Iosevich –
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MATH 591-04 PhD Readings in Math Stephen Kleene –
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MATH 591-05 PhD Readings in Math Naomi Jochnowitz –
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MATH 591-06 PhD Readings in Math Sevak Mkrtchyan –
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MATH 591-07 PhD Readings in Math Jonathan Pakianathan –
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MATH 591-08 PhD Readings in Math Juan Rivera Letelier –
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MATH 591-09 PhD Readings in Math Douglas Ravenel –
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MATH 591-10 PhD Readings in Math Sema Salur –
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MATH 591-11 PhD Readings in Math Thomas Tucker –
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MATH 591-12 PhD Readings in Math Arjun Krishnan –
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MATH 591-13 PhD Readings in Math Xuwen Chen –
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MATH 591-14 PhD Readings in Math Carl Mueller –
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MATH 591-15 PhD Readings in Math Dan Geba –
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MATH 591-16 PhD Readings in Math Dinesh Thakur –
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MATH 591-17 PhD Readings in Math Michael Gage –
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MATH 591-18 PhD Readings in Math Saul Lubkin –
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MATH 591-19 PhD Readings in Math Steven Gonek –
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MATH 595-01 PhD Research in Math Arjun Krishnan –
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MATH 595-02 PhD Research in Math Sevak Mkrtchyan –
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MATH 595-03 PhD Research in Math Stephen Kleene –
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MATH 595-04 PhD Research in Math Doug Haessig –
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MATH 595-05 PhD Research in Math Naomi Jochnowitz –
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MATH 595-06 PhD Research in Math Xuwen Chen –
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MATH 595-07 PhD Research in Math Alex Iosevich –
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MATH 595-08 PhD Research in Math Allan Greenleaf –
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MATH 595-09 PhD Research in Math Carl Mueller –
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MATH 595-10 PhD Research in Math Dan Geba –
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MATH 595-11 PhD Research in Math Dinesh Thakur –
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MATH 595-12 PhD Research in Math Douglas Ravenel –
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MATH 595-13 PhD Research in Math Frederick Cohen –
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MATH 595-14 PhD Research in Math Jonathan Pakianathan –
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MATH 595-15 PhD Research in Math Juan Rivera Letelier –
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MATH 595-16 PhD Research in Math Michael Gage –
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MATH 595-17 PhD Research in Math Saul Lubkin –
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MATH 595-18 PhD Research in Math Sema Salur –
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MATH 595-19 PhD Research in Math Steven Gonek –
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MATH 595-20 PhD Research in Math Thomas Tucker –
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MATH 895-1 Cont of Master's Enrollment – –
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MATH 897-1 Master's Dissertation Naomi Jochnowitz –
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MATH 899-1 Master's Dissertation Naomi Jochnowitz –
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MATH 995-1 Cont of Doctoral Enrollment – –
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MATH 997-01 Doctoral Dissertation Arjun Krishnan –
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MATH 997-02 Doctoral Dissertation Sevak Mkrtchyan –
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MATH 997-03 Doctoral Dissertation Stephen Kleene –
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MATH 997-04 Doctoral Dissertation Doug Haessig –
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MATH 997-05 Doctoral Dissertation Naomi Jochnowitz –
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MATH 997-06 Doctoral Dissertation Xuwen Chen –
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MATH 997-07 Doctoral Dissertation Alex Iosevich –
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MATH 997-08 Doctoral Dissertation Allan Greenleaf –
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MATH 997-09 Doctoral Dissertation Carl Mueller –
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MATH 997-10 Doctoral Dissertation Dan Geba –
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MATH 997-11 Doctoral Dissertation Dinesh Thakur –
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MATH 997-12 Doctoral Dissertation Douglas Ravenel –
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MATH 997-13 Doctoral Dissertation Frederick Cohen –
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MATH 997-14 Doctoral Dissertation Jonathan Pakianathan –
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MATH 997-15 Doctoral Dissertation Juan Rivera Letelier –
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MATH 997-16 Doctoral Dissertation Michael Gage –
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MATH 997-17 Doctoral Dissertation Saul Lubkin –
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MATH 997-18 Doctoral Dissertation Sema Salur –
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MATH 997-19 Doctoral Dissertation Steven Gonek –
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MATH 997-20 Doctoral Dissertation Thomas Tucker –
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MATH 999-01 Doctoral Dissertation Stephen Kleene –
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MATH 999-02 Doctoral Dissertation Arjun Krishnan –
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MATH 999-03 Doctoral Dissertation Sevak Mkrtchyan –
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MATH 999-04 Doctoral Dissertation Doug Haessig –
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MATH 999-05 Doctoral Dissertation Naomi Jochnowitz –
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MATH 999-06 Doctoral Dissertation Xuwen Chen –
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MATH 999-07 Doctoral Dissertation Alex Iosevich –
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MATH 999-08 Doctoral Dissertation Allan Greenleaf –
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MATH 999-09 Doctoral Dissertation Carl Mueller –
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MATH 999-10 Doctoral Dissertation Dan Geba –
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MATH 999-11 Doctoral Dissertation Dinesh Thakur –
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MATH 999-12 Doctoral Dissertation Douglas Ravenel –
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MATH 999-13 Doctoral Dissertation Frederick Cohen –
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MATH 999-14 Doctoral Dissertation Jonathan Pakianathan –
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MATH 999-15 Doctoral Dissertation Juan Rivera Letelier –
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MATH 999-16 Doctoral Dissertation Michael Gage –
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MATH 999-17 Doctoral Dissertation Saul Lubkin –
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MATH 999-18 Doctoral Dissertation Sema Salur –
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MATH 999-19 Doctoral Dissertation Steven Gonek –
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MATH 999-20 Doctoral Dissertation Thomas Tucker –
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Number	Title	Instructor	Time
Monday
Monday and Wednesday
MATH 472-1 Functional Analysis Allan Greenleaf
Banach spaces; dual spaces; Riesz representation theorem; Hilbert spaces; Fourier series; projective and unitary operators; spectral analysis of completely continuous self-adjoint operators. Applications.
MATH 440-1 General Topology Jonathan Pakianathan
Prerequisites: MTH 265 or equivalent. Permission of instructor required for Undergraduates. Description: The first half of the course will study the general topological notions of topological space, metric spaces, quotient spaces, connectedness, compactness, manifolds and topological groups. The second half of the course will be an introduction to the differential topology of smooth manifolds. Topics include Sard’s theorem, transversality, intersection theory and applications such as the Jordan-Brouwer separation theorem, the Borsuk-Ulam theorem and the Poincare-Hopf theorem. This course will not cover the theory of differential forms, distributions or integration on manifolds which is usually covered in our spring graduate differentiable manifolds course instead.
MATH 443-1 Algebraic Topology Douglas Ravenel
Prerequisites: MTH 436 and MTH 440. Permission of instructor required for Undergraduates. Description: The combinatorial structure of complexes and the homology of polyhedra; applications of algebraic techniques in topology to classification of surfaces, fixed point theory, and analysis.
MATH 531-1 Algebraic Num Theory Naomi Jochnowitz
Valuations, ideal theory, divisors. Class number, unit theorem. Geometric applications.
MATH 506-1 Advanced Topics in Probability Theory Carl Mueller
Topics are related to recent research in the field.
MATH 436-1 Algebra I Naomi Jochnowitz
Prerequisites: MTH 237 or equivalent. Undergrads must have permission of Instructor. Description: Rings and modules, group theory, fields and Galois theory.
Monday, Wednesday, and Friday
MATH 549-1 Toric Topology Frederick Cohen
The main direction of this subject is a development of topological spaces known as moment-angle complexes as well as toric manifolds. Moment-angle complexes are unions of products of circles, and 2-disks"indexed" by a finite simplicial complex. Moment-angle complexes admit actions of products of circles with orbit spaces frequently known as toric manifolds. These spaces and their properties are at the interface of topology, geometry, algebraic topology as well as combinatorics. The goal of the course is to develop some of the main structure theorems in the subject. There will be a strong emphasis on examples which will be developed in class.
Tuesday and Thursday
MATH 471-1 Real Analysis Dan Geba
Prerequisites: MTH 265 or equivalent. Description: Lebesgue measure on the line; measure spaces; integration; convergence theorems; Radon-Nikodym theorem; differentiation; Fubini's theorem; function spaces.
MATH 507-1 Advanced Topics in Probability: First and Last Passage Percolation Arjun Krishnan
First-Passage Percolation (FPP) is a simple shortest path problem on a graph: pick a graph; put some random weights on its edges to mimic the time to cross edges; pick any two vertices and _nd the shortest time (weight) path between them. The passage time between vertices is a random metric on the graph, and the shortest-time paths are geodesics for this metric. One usually studies the statistics of the passage time and the behavior of geodesics on Zd. This simple model has incredible connections to 1) the zeros of the zeta function 2) random matrix theory 3) representation theory and combinatorics 4) Hamilton-Jacobi PDEs. The model was proposed in the 60s, but the main questions in the _eld are almost entirely open. In this course, I will loosely follow the review \50 years of _rst-passage percolation", and then move on to the research level questions in towards the end of the course. Along the way, I intend to cover: (1) Shortest path and ow algorithms, (2) Geodesic dynamics through ergodic theory, and (3) Hamilton-Jacobi PDEs and nonlinear eigenvalue problems. The course will be mostly probabilistic and analytic. The prerequisites are the basic real analysis and probability courses: 471 and 406. However, I think you can easily manage if you've only taken one of these.
Friday