Department of Mathematics Calendar

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The Department of Mathematics is a bustling place full of new ideas. We host several events that occur throughout the year, including seminars, colloquium, conferences, and social events. Our seminars and colloquium are open to the public: all students, faculty, or alumni who are interested are welcome to join us for exciting talks on the leading edge of mathematics research!

For information about adding events to this calendar, please see this user guide

Number Theory Seminar

Event Type
Seminar/Symposium
Sponsor
Number Theory Research Group
Location
Zoom
Date
Oct 4, 2022   11:00 am - 12:00 pm  
Speaker
Daniel Martin (U.C. Davis)
Cost
0
Contact
Kevin Ford
E-Mail
ford126@illinois.edu
Views
22

The trouble with Bianchi groups

If O is the ring of integers in a number field, PSL_n(O) is almost always generated by its elementary matrices. The only exceptions are when n=2 and O is non-Euclidean, imaginary quadratic. In these cases, group presentations are computed algorithmically. There is no known, general formulation. That these algorithms eventually terminate (and when they terminate) follows from a bound on the complexity of a Ford domain associated to PSL_2(O). We give a new upper bound on this complexity that comes within a power of log|Δ| of the value in question, where Δ is the discriminant of O.

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