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Noncrossing partitions, braid groups, and complex polynomials Michael Dougherty, Lafayette Abstract: The n-strand braid group is one of the most important objects in geometric group theory, in part because it lies in the overlap of many different classes of groups, including Artin groups and mapping class groups. Topologically, this group can be viewed as the fundamental group for the space of monic complex polynomials with distinct roots, and algebraically it is often defined using a generating set of n-1 diagrams depicting half-twists of adjacent strands. Work of Birman-Ko-Lee, T. Brady, and Bessis around the turn of the century introduced a new generating set for these groups which used the lattice of noncrossing partitions, and the combinatorics of this lattice has led to breakthroughs in our understanding of braid groups and Artin groups more generally. In this talk, I will describe some new connections between noncrossing partitions, braid groups, and complex polynomials. This is joint work with Jon McCammond. Tea and refreshments available from 3:00-3:25 p.m. in the Assmus Conference Room (CU 212).

Dept of Mathematics Spring 2026 Colloquium Series - Professor Sir John Ball

Wed, Apr 1, 2026 3:30pm

Chandler-Ullmann Hall, 218

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Graduate Student Ambassador Virtual Meet & Greet with RSVP Form QR Code and Photo of Ambassadors

Lehigh Engineering: March Virtual Grad Ambassador Panels

Tue, Mar 24, 2026 7:30pm to 8:30pm

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Meet the Grad Ambassadors Flyer. Scan the QR code or click the registration link to rsvp

Lehigh Engineering: Graduate Ambassador Panels

Wed, Feb 11, 2026 7:30pm to 8:30pm

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RCEAS Graduate Student Ambassadors

Lehigh Engineering: Virtual Grad Ambassador Panel

Wed, Dec 17, 2025 7:30pm to 8:30pm

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Engineering Grad Fair, In-Person, Wed Oct 22nd 2:30 - 5:30pm, STEPS Concourse/Lobby

Rossin Graduate School Fair

Wed, Oct 22, 2025 2:30pm to 5:30pm

STEPS Building, Concourse/Lobby

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50th Anniversary Celebration of Polymer Science and Engineering at Lehigh

Tue, Oct 21, 2025

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