MATH 4041
Juan Rivera Letelier
TR 2:00PM  3:15PM

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 Location
 Hylan Building Room 1101 (TR 2:00PM  3:15PM)

MATH 4361
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 4401
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 JordanBrouwer separation theorem, the BorsukUlam theorem and the PoincareHopf 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 4431
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 4711
Dan Geba
TR 9:40AM  10:55AM

Prerequisites: MTH 265 or equivalent. Description: Lebesgue measure on the line; measure spaces; integration; convergence theorems; RadonNikodym theorem; differentiation; Fubini's theorem; function spaces.
 Location
 Hylan Building Room 202 (TR 9:40AM  10:55AM)

MATH 4721
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 selfadjoint operators. Applications.
 Location
 (MW 10:25AM  11:40AM)

MATH 4831
Alex Iosevich
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MATH 4911
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MATH 4921
Doug Haessig
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Prerequisites: Open to firstyear 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, mathsci net, latex, peer support network, etc.

MATH 4931
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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 5041
Carl Mueller
MW 10:25AM  11:40AM

Measure theoretic foundations, the Poisson process, Brownian motion, Markov processes, stochastic integration. Additional topics depending on the interests of the students and professor
 Location
 (MW 10:25AM  11:40AM)

MATH 5061
Carl Mueller
MW 3:25PM  4:40PM

Topics are related to recent research in the field.
 Location
 (MW 3:25PM  4:40PM)

MATH 5071
Arjun Krishnan
TR 9:40AM  10:55AM

FirstPassage 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 shortesttime 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) HamiltonJacobi 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 _rstpassage 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) HamiltonJacobi 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 5311
Naomi Jochnowitz
MW 2:00PM  3:15PM

Valuations, ideal theory, divisors. Class number, unit theorem. Geometric applications.
 Location
 (MW 2:00PM  3:15PM)

MATH 5491
Frederick Cohen
MWF 11:50AM  12:40PM

The main direction of this subject is a development of topological spaces known as momentangle complexes as well as toric manifolds. Momentangle complexes are unions of products of circles, and 2disks"indexed" by a finite simplicial complex. Momentangle 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 5681
Dinesh Thakur
TR 3:25PM  4:40PM

This course starts with the definitions and introductory theory of modular forms, presents an overview of some of the classic papers on the subject, and focuses in on some of the recent advances. Particular topics chosen each year are left up to the individual instructor.
 Location
 Hylan Building Room 1101 (TR 3:25PM  4:40PM)

MATH 5691
Steven Gonek
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Selected topics in nonmultiplicative analytic number theory considered on a seminar basis.

MATH 5731
Allan Greenleaf
TR 9:40AM  12:20PM

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 Location
 (TR 9:40AM  12:20PM)

MATH 5901
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MATH 59101
Frederick Cohen
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MATH 59102
Allan Greenleaf
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MATH 59103
Alex Iosevich
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MATH 59104
Stephen Kleene
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MATH 59105
Naomi Jochnowitz
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MATH 59106
Sevak Mkrtchyan
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MATH 59107
Jonathan Pakianathan
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MATH 59108
Juan Rivera Letelier
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MATH 59109
Douglas Ravenel
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MATH 59110
Sema Salur
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MATH 59111
Thomas Tucker
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MATH 59112
Arjun Krishnan
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MATH 59113
Xuwen Chen
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MATH 59114
Carl Mueller
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MATH 59115
Dan Geba
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MATH 59116
Dinesh Thakur
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MATH 59117
Michael Gage
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MATH 59118
Saul Lubkin
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MATH 59119
Steven Gonek
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MATH 59501
Arjun Krishnan
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MATH 59502
Sevak Mkrtchyan
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MATH 59503
Stephen Kleene
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MATH 59504
Doug Haessig
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MATH 59505
Naomi Jochnowitz
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MATH 59506
Xuwen Chen
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MATH 59507
Alex Iosevich
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MATH 59508
Allan Greenleaf
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MATH 59509
Carl Mueller
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MATH 59510
Dan Geba
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MATH 59511
Dinesh Thakur
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MATH 59512
Douglas Ravenel
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MATH 59513
Frederick Cohen
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MATH 59514
Jonathan Pakianathan
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MATH 59515
Juan Rivera Letelier
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MATH 59516
Michael Gage
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MATH 59517
Saul Lubkin
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MATH 59518
Sema Salur
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MATH 59519
Steven Gonek
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MATH 59520
Thomas Tucker
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MATH 8951
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MATH 8971
Naomi Jochnowitz
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MATH 8991
Naomi Jochnowitz
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MATH 9851
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MATH 9951
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MATH 99701
Arjun Krishnan
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MATH 99702
Sevak Mkrtchyan
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MATH 99703
Stephen Kleene
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MATH 99704
Doug Haessig
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MATH 99705
Naomi Jochnowitz
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MATH 99706
Xuwen Chen
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MATH 99707
Alex Iosevich
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MATH 99708
Allan Greenleaf
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MATH 99709
Carl Mueller
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MATH 99710
Dan Geba
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MATH 99711
Dinesh Thakur
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MATH 99712
Douglas Ravenel
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MATH 99713
Frederick Cohen
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MATH 99714
Jonathan Pakianathan
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MATH 99715
Juan Rivera Letelier
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MATH 99716
Michael Gage
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MATH 99717
Saul Lubkin
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MATH 99718
Sema Salur
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MATH 99719
Steven Gonek
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MATH 99720
Thomas Tucker
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MATH 99901
Stephen Kleene
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MATH 99902
Arjun Krishnan
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MATH 99903
Sevak Mkrtchyan
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MATH 99904
Doug Haessig
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MATH 99905
Naomi Jochnowitz
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MATH 99906
Xuwen Chen
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MATH 99907
Alex Iosevich
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MATH 99908
Allan Greenleaf
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MATH 99909
Carl Mueller
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MATH 99910
Dan Geba
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MATH 99911
Dinesh Thakur
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MATH 99912
Douglas Ravenel
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MATH 99913
Frederick Cohen
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MATH 99914
Jonathan Pakianathan
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MATH 99915
Juan Rivera Letelier
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MATH 99916
Michael Gage
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MATH 99917
Saul Lubkin
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MATH 99918
Sema Salur
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MATH 99919
Steven Gonek
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MATH 99920
Thomas Tucker
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