Graduate Program

Term Schedule

Fall 2021

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 Hylan Building Room 206 (MW 4:50PM - 6:05PM)
MATH 440-1 General Topology Frederick Cohen MWF 11:50AM - 12:40PM
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 Hylan Building Room 1106A (MWF 11:50AM - 12:40PM)
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 Hylan Building Room 206 (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 101 (TR 9:40AM - 10:55AM)
MATH 472-1 Functional Analysis Xuwen Chen 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 Hylan Building Room 206 (MW 10:25AM - 11:40AM)
MATH 483-1 2nd Year Grad Orientation Alex Iosevich –
Blank Description
MATH 492-1 Grad Professional Seminar Allan Greenleaf –
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 504-1 Stochastic Process Arjun Krishnan TR 12:30PM - 1:45PM
Discrete and continuous time Markov chains, Poisson processes, Brownian motion, stochastic calculus. One optional topic like branching processes, percolation, interacting particle systems, or potential theory. Location (TR 12:30PM - 1:45PM)
MATH 549-2 Topics in Algebraic Topology: The Cohomology of Groups Jonathan Pakianathan TR 2:00PM - 3:15PM
Prerequisites: Familiarity with abstract algebra (either (MTH236H and MTH237) or (MTH436 and MTH437) or equivalent) and algebraic topology (MTH 443 or equivalent) is required. Description: The cohomology of groups is an area that lies at the intersection of topology, geometry, algebra and number theory. To every group, there is a unique classifying space (up to homotopy equivalence) that encodes the symmetries of the group and the cohomology of this space is called the cohomology of the group. This invariant is very useful in constraining the behaviour of group actions of that group on any object, whether the object is a space, a graph, a linear representation or a field extension in Galois theory. This course will study the basic properties of group cohomology and some of the fundamental computations. We will introduce the basic homological algebra, transfer and spectral sequence techniques needed to do the basic computations as well as the notion of equivariant cohomology to study questions related to group actions. We will also study a variant for finite groups called Tate cohomology. We will then apply this invariant to study some questions in topology, geometry and number theory. Location (TR 2:00PM - 3:15PM)
MATH 591-01 PhD Readings in Math Frederick Cohen –
Blank Description
MATH 591-02 PhD Readings in Math Allan Greenleaf –
Blank Description
MATH 591-03 PhD Readings in Math Alex Iosevich –
Blank Description
MATH 591-04 PhD Readings in Math Stephen Kleene –
Blank Description
MATH 591-05 PhD Readings in Math Naomi Jochnowitz –
Blank Description
MATH 591-06 PhD Readings in Math Sevak Mkrtchyan –
Blank Description
MATH 591-07 PhD Readings in Math Jonathan Pakianathan –
Blank Description
MATH 591-08 PhD Readings in Math Juan Rivera Letelier –
Blank Description
MATH 591-09 PhD Readings in Math Douglas Ravenel –
Blank Description
MATH 591-10 PhD Readings in Math Sema Salur –
Blank Description
MATH 591-11 PhD Readings in Math Thomas Tucker –
Blank Description
MATH 591-12 PhD Readings in Math Arjun Krishnan –
Blank Description
MATH 591-13 PhD Readings in Math Xuwen Chen –
Blank Description
MATH 591-14 PhD Readings in Math Carl Mueller –
Blank Description
MATH 591-15 PhD Readings in Math Dan Geba –
Blank Description
MATH 591-16 PhD Readings in Math Dinesh Thakur –
Blank Description
MATH 591-17 PhD Readings in Math Michael Gage –
Blank Description
MATH 591-18 PhD Readings in Math Saul Lubkin –
Blank Description
MATH 591-19 PhD Readings in Math Steven Gonek –
Blank Description
MATH 595-01 PhD Research in Math Arjun Krishnan –
Blank Description
MATH 595-02 PhD Research in Math Sevak Mkrtchyan –
Blank Description
MATH 595-03 PhD Research in Math Stephen Kleene –
Blank Description
MATH 595-04 PhD Research in Math Doug Haessig –
Blank Description
MATH 595-05 PhD Research in Math Naomi Jochnowitz –
Blank Description
MATH 595-06 PhD Research in Math Xuwen Chen –
Blank Description
MATH 595-07 PhD Research in Math Alex Iosevich –
Blank Description
MATH 595-08 PhD Research in Math Allan Greenleaf –
Blank Description
MATH 595-09 PhD Research in Math Carl Mueller –
Blank Description
MATH 595-10 PhD Research in Math Dan Geba –
Blank Description
MATH 595-11 PhD Research in Math Dinesh Thakur –
Blank Description
MATH 595-12 PhD Research in Math Douglas Ravenel –
Blank Description
MATH 595-13 PhD Research in Math Frederick Cohen –
Blank Description
MATH 595-14 PhD Research in Math Jonathan Pakianathan –
Blank Description
MATH 595-15 PhD Research in Math Juan Rivera Letelier –
Blank Description
MATH 595-16 PhD Research in Math Michael Gage –
Blank Description
MATH 595-17 PhD Research in Math Saul Lubkin –
Blank Description
MATH 595-18 PhD Research in Math Sema Salur –
Blank Description
MATH 595-19 PhD Research in Math Steven Gonek –
Blank Description
MATH 595-20 PhD Research in Math Thomas Tucker –
Blank Description
MATH 895-1 Cont of Master's Enrollment – –
Blank Description
MATH 897-1 Master's Dissertation Naomi Jochnowitz –
Blank Description
MATH 899-1 Master's Dissertation Naomi Jochnowitz –
Blank Description
MATH 995-1 Cont of Doctoral Enrollment – –
Blank Description
MATH 997-01 Doctoral Dissertation Arjun Krishnan –
Blank Description
MATH 997-02 Doctoral Dissertation Sevak Mkrtchyan –
Blank Description
MATH 997-03 Doctoral Dissertation Stephen Kleene –
Blank Description
MATH 997-04 Doctoral Dissertation Doug Haessig –
Blank Description
MATH 997-05 Doctoral Dissertation Naomi Jochnowitz –
Blank Description
MATH 997-06 Doctoral Dissertation Xuwen Chen –
Blank Description
MATH 997-07 Doctoral Dissertation Alex Iosevich –
Blank Description
MATH 997-08 Doctoral Dissertation Allan Greenleaf –
Blank Description
MATH 997-09 Doctoral Dissertation Carl Mueller –
Blank Description
MATH 997-10 Doctoral Dissertation Dan Geba –
Blank Description
MATH 997-11 Doctoral Dissertation Dinesh Thakur –
Blank Description
MATH 997-12 Doctoral Dissertation Douglas Ravenel –
Blank Description
MATH 997-13 Doctoral Dissertation Frederick Cohen –
Blank Description
MATH 997-14 Doctoral Dissertation Jonathan Pakianathan –
Blank Description
MATH 997-15 Doctoral Dissertation Juan Rivera Letelier –
Blank Description
MATH 997-16 Doctoral Dissertation Michael Gage –
Blank Description
MATH 997-17 Doctoral Dissertation Saul Lubkin –
Blank Description
MATH 997-18 Doctoral Dissertation Sema Salur –
Blank Description
MATH 997-19 Doctoral Dissertation Steven Gonek –
Blank Description
MATH 997-20 Doctoral Dissertation Thomas Tucker –
Blank Description
MATH 999-01 Doctoral Dissertation Stephen Kleene –
Blank Description
MATH 999-02 Doctoral Dissertation Arjun Krishnan –
Blank Description
MATH 999-03 Doctoral Dissertation Sevak Mkrtchyan –
Blank Description
MATH 999-04 Doctoral Dissertation Doug Haessig –
Blank Description
MATH 999-05 Doctoral Dissertation Naomi Jochnowitz –
Blank Description
MATH 999-06 Doctoral Dissertation Xuwen Chen –
Blank Description
MATH 999-07 Doctoral Dissertation Alex Iosevich –
Blank Description
MATH 999-08 Doctoral Dissertation Allan Greenleaf –
Blank Description
MATH 999-09 Doctoral Dissertation Carl Mueller –
Blank Description
MATH 999-10 Doctoral Dissertation Dan Geba –
Blank Description
MATH 999-11 Doctoral Dissertation Dinesh Thakur –
Blank Description
MATH 999-12 Doctoral Dissertation Douglas Ravenel –
Blank Description
MATH 999-13 Doctoral Dissertation Frederick Cohen –
Blank Description
MATH 999-14 Doctoral Dissertation Jonathan Pakianathan –
Blank Description
MATH 999-15 Doctoral Dissertation Juan Rivera Letelier –
Blank Description
MATH 999-16 Doctoral Dissertation Michael Gage –
Blank Description
MATH 999-17 Doctoral Dissertation Saul Lubkin –
Blank Description
MATH 999-18 Doctoral Dissertation Sema Salur –
Blank Description
MATH 999-19 Doctoral Dissertation Steven Gonek –
Blank Description
MATH 999-20 Doctoral Dissertation Thomas Tucker –
Blank Description

Number	Title	Instructor	Time
Monday
Monday and Wednesday
MATH 472-1 Functional Analysis Xuwen Chen
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 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 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 440-1 General Topology Frederick Cohen
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.
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 504-1 Stochastic Process Arjun Krishnan
Discrete and continuous time Markov chains, Poisson processes, Brownian motion, stochastic calculus. One optional topic like branching processes, percolation, interacting particle systems, or potential theory.
MATH 549-2 Topics in Algebraic Topology: The Cohomology of Groups Jonathan Pakianathan
Prerequisites: Familiarity with abstract algebra (either (MTH236H and MTH237) or (MTH436 and MTH437) or equivalent) and algebraic topology (MTH 443 or equivalent) is required. Description: The cohomology of groups is an area that lies at the intersection of topology, geometry, algebra and number theory. To every group, there is a unique classifying space (up to homotopy equivalence) that encodes the symmetries of the group and the cohomology of this space is called the cohomology of the group. This invariant is very useful in constraining the behaviour of group actions of that group on any object, whether the object is a space, a graph, a linear representation or a field extension in Galois theory. This course will study the basic properties of group cohomology and some of the fundamental computations. We will introduce the basic homological algebra, transfer and spectral sequence techniques needed to do the basic computations as well as the notion of equivariant cohomology to study questions related to group actions. We will also study a variant for finite groups called Tate cohomology. We will then apply this invariant to study some questions in topology, geometry and number theory.
Friday