Department Colloquium
Fall 2026
Regular Day: Thursday
Regular Time: 4:00PM - 5:00PM
Regular Location: LCB 115
| Date | Speaker | Talk Information | Details |
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September 3 |
Yuchen Liu
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The classification of algebraic varieties naturally leads to moduli questions: how do varieties of a given type vary in families, and how can they be compactified? A basic organizing principle is the positivity of the canonical bundle, which leads to the three broad classes of varieties of general type, Fano varieties, and Calabi–Yau varieties. In dimension one, this picture is already familiar from the theory of moduli of curves.
In this talk, we will discuss the higher-dimensional story. For varieties of general type, we will review the KSBA theory and its use of stable varieties to construct compact moduli spaces. For Fano varieties, we will discuss K-stability and the resulting theory of K-moduli. We will then turn to Calabi–Yau varieties, where the moduli problem is closely related to Hodge theory and mirror symmetry, and discuss recent progress toward compactifications, as well as some open problems and future directions.
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September 17 |
Zhouli Xu
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I will survey on the Kervaire invariant problem and discuss the recent solution of the final case in dimension 126, joint work with W. Lin and G. Wang.
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September 24 |
Helen Moore
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Finding a treatment regimen that increases median patient survival time by 5% means extra time with loved ones for patients. It can also mean the difference between clinical trial success and failure for a new therapy. In the past, trial and error was used to find treatment regimens that yield better patient outcomes. Now we have mechanistic mathematical models of disease-therapy dynamics that can help. Optimization methods can predict regimens expected to achieve the best outcomes; these regimens can then be tested experimentally and clinically. This can be especially helpful when there are many possible different combinations to consider, or when optimal regimens are counterintuitive. I will make the case that counterintuitive solutions can be best in the real world, for both airplanes and treatment regimens, and that we may be missing out on substantial patient benefit when we don’t calculate optimal regimens for our disease models.
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October 1 |
Jordan Ellenberg
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TBA
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October 29 |
Vijaylaxmi Trivedi
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TBA
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November 5 |
Alex Cloninger
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TBA
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November 12 |
Justin Solomon
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TBA
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November 19 |
Jared Weinstein
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TBA
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December 10 |
Volodia Nekrashevych
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TBA
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