This is the homepage for the 2020 Summer Minicourses, a series of week-long graduate student-run minicourses at UT Austin.
This summer, the minicourses are being organized by Desmond Coles, Arun Debray, Zachary Gardner, and Richard Wong. You can contact us at SMC.Organizers@gmail.com.
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Please check the schedule for updated abstracts and minicourse times. Meeting links for the minicourses will be sent to the mailing list and posted in the appropriate Slack channel.
If you are interested in participating in a minicourse, click here to join the SMC Slack. You must then join the Minicourse channels that you're interested in.
Some minicourses have limits on the number of participants. If you are interested in a participant-limited minicourse, please fill out the interest form.
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Current Course: Introduction to the Geometric Langlands Correspondence
Speaker: Tom Gannon
Dates, Time, and Location: Aug 17-21, 2-3:30PM CDT, Zoom link available in the Slack channel.
Abstract: In this mini course, we'll provide context and give motivation related to the Geometric Langlands conjecture. We will start off by discussing the Langlands correspondence for the group GL_1, which is also known as class field theory. We will then discuss what the Langlands correspondence says for general reductive groups G for function fields. After that, we will talk about the generalization of this correspondence to the Geometric Langlands conjecture, which will lead us to the notion of a Hecke eigensheaf. We will then discuss why the naive Geometric Langlands conjecture is false, and how it can be corrected with the notion of indcoherent sheaves with nilpotent singular support. Time and interest permitting, we will also discuss the notion of an oper and the construction of a Hecke eigensheaf associated to an oper or discuss the local geometric Langlands program.
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Minicourses focus on tools, methods, and ideas that aren't usually covered in prelims but are useful in topics classes/research. The idea is that a week-long minicourse will remain engaging, be easier to schedule, and help provide focus. These courses are primarily for graduate students, but all are welcome to participate!
Past courses have included:
- Review of classes that were taught in previous years.
- Primers for classes that will be taught next year.
- Examples of useful computational tools.
- Introductions to a subject/research area.
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These courses were inspired in large part by the ones held at University of Michigan, which were started by Takumi Murayama.
You can click here to be added to the email list, click here to join the slack channel, and click here to add the schedule to your calendar.