Except where (frequently) noted to the contrary, the seminar meets from 4:30-5:30 every other Tuesday in Krieger 306.
September 12 Speaker: Michael Lipnowski (IAS) Title: Growth of the smallest 1-form eigenvalue on hyperbolic manifolds and applications to torsion homology growth Abstract: Joint work with Mark Stern.
We relate small 1-form eigenvalues to relative cycle complexity on hyperbolic manifolds: small eigenvalues correspond to closed geodesics no multiple of which bounds a surface of small genus. We describe potential applications of this equivalence principle toward proving optimal torsion homology growth in families of congruence, arithmetic hyperbolic 3-manifolds.
October 10 Speaker: Jessica Fintzen (Michigan) Title: On the Moy-Prasad filtration and supercuspidal representations Abstract: Reeder and Yu gave recently a new construction of certain supercuspidal representations of p-adic reductive groups (called epipelagic representations). Their construction relies on the existence of stable vectors in the first Moy-Prasad filtration quotient under the action of a reductive quotient. We will explain these ingredients and present a theorem about the existence of such stable vectors for all primes p. This builds on a result of Reeder and Yu about the existence of stable vectors for large primes and generalizes the paper of the speaker and Romano, which treats the case of an absolutely simple split reductive group.
If time permits, we will present the underlying general set-up that allows us to compare the Moy-Prasad filtration representations for different primes p. This provides a tool to transfer results about the Moy-Prasad filtration from one prime to arbitrary primes and also yields new descriptions of the Moy-Prasad filtration representations.
SPECIAL TIME AND ROOM: October 26 (Thursday), 3:00 in Maryland 201 Speaker: Lucia Mocz (Princeton) Title: Abstract:
SPECIAL TIME AND ROOM: November 2 (Thursday), 3:00 in Maryland 201 Speaker: Eric Katz (OSU) Title: Abstract:
SPECIAL TIME AND ROOM: November 14, Room TBA Speaker: Xuhua He (Maryland) Title: Abstract:
November 28 Speaker: Yiannis Sakellaridis (Rutgers Newark) Title: Abstract: