All semesters: Spring 2025, Fall 2024 , Spring 2024, Fall 2023, Spring 2023, Fall 2022
Tuesdays 4-6, Evans 939
| date | speaker | title | abstract |
|---|---|---|---|
| 1/14 | Daniel Erman | Long Live the King (Conjecture) | The King Conjecture proposed that every toric variety has a full, strong exceptional collection of line bundles. While the conjecture turned out to be false, it has continued to inspire a huge amount of research on derived categories of toric varieties. I will explain how King’s Conjecture can be remedied, and proven, if one incorporates a birational geometry perspective. |
| Eric Larson | Normal bundles of rational curves in Grassmannians | Let $C$ be a general rational curve of degree $d$ in a Grassmannian $G(k, n)$. The natural expectation is that its normal bundle is balanced, i.e., isomorphic to $\bigoplus O(e_i)$ with all $|e_i - e_j| \leq 1$. In this talk, I will describe several counterexamples to this expectation, propose a suitably revised conjecture, and describe recent progress towards this conjecture. | |
| 1/21 | Reed Jacobs | Borel-Weil Theory through Examples | Let \(V\) be the standard representation of \(\operatorname{SL}_2(\mathbb{C})\) acting on \(\mathbb{C}^2\).
One of the first theorems proved in a Lie theory course is that all the irreducible representations of \(\operatorname{SL}_2(\mathbb{C})\) are given by the symmetric powers \(V(n) := \operatorname{Sym}^n(V)\).
\(V(n)\) is the vector space of homogeneous degree \(n\) polynomials in \(2\) variables; this is also the global sections of the holomorphic line bundle \(\mathcal{O}(n)\) on \(\mathbb{C}\mathbb{P}^1\)!
This is the simplest example of Borel-Weil-Bott theory, which says all representations of complex semisimple Lie groups arise from the cohomology of holomorphic line bundles on a space constructed from the Lie group. I will review just enough Lie theory to state this, explain the construction, and do some simple examples. |
| Ben Church | Title 2 | Abstract 2 | |
| 1/28 | Mahrud Sayrafi | Title 1 | Abstract 1 |
| Eugene Gorskiy | Title 2 | Abstract 2 | |
| 2/4 | Speaker 1 | Title 1 | Abstract 1 |
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| 2/11 | Speaker 1 | Title 1 | Abstract 1 |
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| 2/18 | Speaker 1 | Title 1 | Abstract 1 |
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| 2/25 | Speaker 1 | Title 1 | Abstract 1 |
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| 3/4 | Speaker 1 | Title 1 | Abstract 1 |
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| 3/11 | Christopher O'Neill | Title 1 | Abstract 1 |
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| 3/18 | Joe Harris | Title 1 | Abstract 1 |
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| 3/25 | No seminar -- spring break | ||
| 4/1 | Speaker 1 | Title 1 | Abstract 1 |
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| 4/8 | Speaker 1 | Title 1 | Abstract 1 |
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| 4/15 | Speaker 1 | Title 1 | Abstract 1 |
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| 4/22 | Speaker 1 | Title 1 | Abstract 1 |
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| 4/29 -- last meeting of the semester | Speaker 1 | Title 1 | Abstract 1 |
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