Colloquia: Difference between revisions
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```Symmetries in Algebraic Geometry and Cremona transformations''' | |||
In this talk I will discuss symmetries of complex algebraic varieties. When studying a projective variety $X$, one usually wants to understand its symmetries. Conversely, the structure of the group of automorphisms of $X$ encodes relevant geometric properties of $X$. After describing some examples of automorphism groups of projective varieties, I will discuss why the notion of automorphism is too rigid in the scope of birational geometry. We are then led to consider another class of symmetries of $X$, its birational self-maps. Birational self-maps of the projective space $\mathbb{P}^n$ are called Cremona transformations. Describing the structure of the group of Cremona transformations of the plane is a classical problem that goes back to the 19th century. In higher dimensions, not so much is known, and a natural problem is to construct interesting subgroups of the Cremona group. I will end by discussing a recent work with Alessio Corti and Alex Massarenti, where we investigate subgroups of the Cremona group consisting of symmetries preserving some special meromorphic volume forms. | |||
== October 23, 2020, [http://www.math.toronto.edu/quastel/ Jeremy Quastel] (University of Toronto) == | == October 23, 2020, [http://www.math.toronto.edu/quastel/ Jeremy Quastel] (University of Toronto) == | ||
Revision as of 01:25, 29 September 2020
UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm.
Fall 2020
September 25, 2020, Joseph Landsberg (Texas A&M)
(Hosted by Gurevitch)
From theoretic computer science to algebraic geometry: how the complexity of matrix multiplication led me to the Hilbert scheme of points.
In 1968 Strassen discovered the way we multiply nxn matrices (row/column) is not the most efficient algorithm possible. Subsequent work has led to the astounding conjecture that as the size n of the matrices grows, it becomes almost as easy to multiply matrices as it is to add them. I will give a history of this problem and explain why it is natural to study it using algebraic geometry and representation theory. I will conclude by discussing recent exciting developments that explain the second phrase in the title.
October 9, 2020, Carolina Araujo (IMPA)
(Hosted by Ellenberg)
```Symmetries in Algebraic Geometry and Cremona transformations
In this talk I will discuss symmetries of complex algebraic varieties. When studying a projective variety $X$, one usually wants to understand its symmetries. Conversely, the structure of the group of automorphisms of $X$ encodes relevant geometric properties of $X$. After describing some examples of automorphism groups of projective varieties, I will discuss why the notion of automorphism is too rigid in the scope of birational geometry. We are then led to consider another class of symmetries of $X$, its birational self-maps. Birational self-maps of the projective space $\mathbb{P}^n$ are called Cremona transformations. Describing the structure of the group of Cremona transformations of the plane is a classical problem that goes back to the 19th century. In higher dimensions, not so much is known, and a natural problem is to construct interesting subgroups of the Cremona group. I will end by discussing a recent work with Alessio Corti and Alex Massarenti, where we investigate subgroups of the Cremona group consisting of symmetries preserving some special meromorphic volume forms.
October 23, 2020, Jeremy Quastel (University of Toronto)
(Hosted by Gorin)
November 6, 2020, Yiannis Sakellaridis (Johns Hopkins University)
(Hosted by Gurevitch)
November 20, 2020, TBA
December 4, 2020, Federico Ardila (San Francisco)
(Hosted by Ellenberg)