Our number theory seminar slot is sometimes unoccupied (the next such date is January 23rd). We will begin filling these empty slots with "Number Theory Lab Meeting".
This is aimed at creating a research community, especially for the benefit of our graduate students, but it will be of interest to all the number theorists and aspiring or closet number theorists in the department and so I wanted to make an announcement to the whole department. Young students who are considering number theory as their future track are especially invited, of course. You'll see it listed in the seminar calendar under the number theory seminar, and more information follows below.
The basic design is modelled after CSU's "lab meeting". It's fluid and adaptable, but the basic structure, at least to start, is:
11-11:10 - tea and informal chatter
11:10 - progress reports (we'll go around the room and everyone can give an update on what they are doing, mostly research, but also relevant may be pedagogy, job applications, etc.)
after that - a totally informal 20 minute chalk talk by one member of the group, about their research interests (background, for now, later after we are all more familiar, maybe recent results).
There are enough of us that I expect we may all get to speak approximately once per semester. We'll ask for volunteers as we rotate through so you have some warning/choice about when your turn is coming. This is friendly, and not meant to add pressure.
When interest dictates, the time can be used for other things, like career discussions, practice talks, trying out a cool number theory outreach activity, learning Sage together, whatever comes up.
I'll (Kate Stange) happily take the first slot and give some background on a problem I'm interested in on January 23rd. Your job is to show up and ask a ton of questions.
Number Theory Lab Meeting
Feb. 06, 2018 1pm (MATH 220)
Grad Algebra/Logic
Peter Mayr (CU Boulder) Supernilpotent algebras 3
Feb. 06, 2018 2pm (MATH 350)
Lie Theory
Nat Thiem (CU)
X
The partition algebra is a classical diagram algebra arising out of Schur—Weyl duality in representation theory. While there are numerous approaches to constructing a -deformation of the partition algebra, they each seem to have had different obstructions. This talk will review the partition algebra, its possible generalizations, and then focus on one particular version that has seen some recent progress. We recover some possibly new combinatorial objects called splatters, which are a generalization of set partitions. This work is joint work with Tom Halverson.
Gromov-Witten theory gives a way of defining enumerative invariants of a smooth complex variety X by, roughly, counting the number of curves on X satisfying various constraints. If two varieties X and Y have similar geometries, say they are birational, it is natural to wonder how their Gromov-Witten invariants relate to one another. Many conjectures and results along these lines have dealt with the case where X and Y are K-equivalent or related by crepant transformation. In joint work with Acosta, we extend these results, in the toric case, to more general birational transformations. Given two complete toric orbifolds X and Y related by wall crossing under variation of GIT, we prove that certain Gromov-Witten generating functions are related by linear transformation and asymptotic expansion. This generalizes the relationship described by the crepant transformation conjecture to the non-crepant setting.
Gromov-Witten theory of toric birational transformations
Number Theory Lab Meeting