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The Rutgers–Newark Graduate Mathematics Seminar (RNGMS) is a weekly seminar for graduate students and friends of the department, kindly supported by the Graduate Student Government Association (GSGA).
Talks range from expository introductions to research-level topics in pure mathematics and applied mathematics, and more. Everyone
is welcome — please join us!
Fall 2026 schedule: Fridays 5:00-6:00 p.m., except holidays
Fall 26 talks:
No talks for the first two weeks because of qualifying exams!
Sept 25, 2026
Title: Principal G-bundles and the classifying space, I
Speaker: Allen Bao
Abstract: We introduce principal G-bundles, a geometric structure on topological spaces widely used in topology and geometry. The classifying space is a topological space representing the functor taking a space to its set of principal bundles. We introduce the classifying space.
Oct 2, 2026
Title: Principal bundles and classifying spaces, II
Speaker: Allen Bao
Abstract: Following last time, we continue discussing classifying spaces some basic applications.
Oct 9, 2026
Title: The Topograph of a Binary Quadratic Form, I
Speaker: Jose A Urrea
Abstract: Binary quadratic forms arise naturally from norms in quadratic number fields and provide a bridge between algebra and integer equations. This talk introduces rings of integers, explores the associated norm forms, and uses Pell’s equation as a concrete example of the arithmetic they encode.
Oct 16, 2026
Title: The Topograph of a Binary Quadratic Form, II
Speaker: Jose A Urrea
Abstract: Building on our discussion of norms and Pell’s equation, we will explore Conway’s topograph, a geometric way to study binary quadratic forms. By arranging the values of a form on a tree, we will see how a simple local rule reveals global arithmetic patterns. We will introduce the wells of positive-definite forms and the rivers of indefinite forms, and connect these pictures to Pell’s equation.
Oct 23, 2026
Title: Equivalence relations in 4-manifold topology
Speaker: Yikai Teng
Abstract: In this talk, we introduce various equivalence relations central to the study of 4-manifold topology. We will focus on h-cobordisms, and explain why smooth h-cobordism theorem fails and reduces to Wall’s stabilization theorem in dimension 4.
Oct 30, 2026
Title: Circuit lower bounds, matrix rigidity and Legendre Symbols
Speaker: Kirill Khvenkin
Abstract: I will briefly introduce each of these topics and explain how they are connected.
Nov 6, 2026
Title: Two Sides of Compact Lie Groups: The Peter–Weyl Theorem, I
Speaker: Qixuan Fang
Abstract: In this talk, we introduce basics in the representation theory of compact Lie groups, in particular, using Haar’s measure to obtain completely reducibility and Schur’s orthogonality, then we explain the Peter-Weyl theorem, the core result in this aspect.
Nov 13, 2026
Title: Two Sides of Compact Lie Groups: The Peter–Weyl Theorem, II
Speaker: Qixuan Fang
Abstract: We skectch a proof of the Peter-Weyl theorem by the spectral theorem for self-adjoint elliptic operators on closed manifolds. In particular, we shall see how for a bi-invariant metric, irreducible representations classified by highest weights correspond to eigenfunctions of the Laplacian, with eigenvalues determined by the Casimir element.
Nov 20, 2026
Title:
Speaker: TBA
Abstract:
Nov 27, 2026
Thanksgiving Recess, no talk
Dec 4, 2026
Title:
Speaker:
Abstract:
Spring 26 Special Session: Homological Algebra Mini-Course
For questions, email the organizers at graduatemath543@gmail.com, or at qixuan.fang@rutgers.edu