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Apr 2

George Mason Giving Day 2026: Asking Mason Nation to lace up for community impact

Apr 2, 2026, 9:00 AM - 9:30 PM

Apr 2

2 Apr (GEOL) Arlo Weil, Structural Geology

Apr 2, 2026, 4:30 - 5:30 PM

Apr 3

Analysis Seminar: Percolation, The Loop O(1) Model, And Beyond

Apr 3, 2026, 11:30 AM - 12:30 PM

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Geometry MMA Seminar: Representation varieties of RAAGs

Apr 3, 2026, 1:30 - 2:30 PM

 

Speaker:  Anunoy Chakraborty (GMU)

Title: Representation varieties of RAAGs

 

Abstract:   In this talk, we study the character varieties of right-angled Artin groups (RAAGs) into compact Lie groups and analyze how the algebraic structure of the target group influences the topology of these moduli spaces. For a broad class of compact, connected Lie groups including Special Unitary Group SU(n) and Unitary Group U(n), we prove that the corresponding representation varieties of RAAGs are connected. In contrast, we show that for other large families, such as Special Orthogonal Group SO(n) and Spin Group Spin(n) for n ≥ 3, these varieties are typically disconnected, revealing a sharp distinction driven by the topology of the target group. We further examine star-shaped RAAGs with ℓ leaves and describe the geometry of their SU(2) character varieties. We show that the regular locus forms a trivial bundle over an interval, with fibers homeomorphic to the SU(2) character variety of a free abelian group of rank ℓ. In the special case ℓ = 2, we prove that the SU(2) character variety deformation retracts to the 3-sphere, S3. We then show that the action of the Out(Γℓ) on these character varieties does not admit an ergodic measure of full support.

 

Time:  Friday, April 3, 2026 – 1:30pm-2:30pm

Place: Exploratory Hall, Room 4208

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