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## February 2021

### Eric Vanden-Eijnden, Courant Institute – Mathematics Colloquium

Speaker: Eric Vanden-Eijnden (Courant Institute) Time: 4pm, 02/25/2021 Zoom Meeting Id: 969 9584 1746 Passcode: 908333 Title: Trainability and accuracy of artificial neural networks Abstract: The recent success of machine learning suggests that neural networks may be capable of approximating high-dimensional functions with controllably small errors. As a result, they could outperform standard function interpolation methods that have been the workhorses of scientific computing but do not scale well with dimension. In support of this prospect, here I will review…

Find out more »## March 2021

### Andrei Okounkov, Columbia University – Mathematics Colloquium

Andrei Okounkov, Columbia University Title: Interpolation, q-difference equations, and curve counting Abstract: There is an interesting topology behind such classical questions as interpolation and solving linear q-difference equations by integrals. It has to do with counting algebraic curves in some very specific geometries, which can be also phrased as computing indices in certain (2+1) dimensional supersymmetric QFTs. The talk will be an introduction to this circle of ideas.

Find out more »### Anne Dranowski, IAS – Geometric Methods in Representation Theory Seminar

Anne Dranowski, IAS Title: How to compute the fusion product of MV cycles in type A Abstract: In their recent paper on the MV basis and DH measures, Baumann, Kamnitzer and Knutson showed that Mirkovic and Vilonen’s geometric Satake basis of singular algebraic cycles yields a biperfect basis of the coordinate ring of a unipotent subgroup. Moreover, they showed that the structure constants of multiplication of basis vectors in this ring are given by intersection forms. We present joint work…

Find out more »### Hongkai Zhao, Duke University – Applied Mathematics Seminar

Hongkai Zhao, Duke University Title: Model Complexity And Its Implications To Forward and Inverse Problems Abstract: In this talk I will present different ways to study model complexity for partial dierential equation (PDE) based forward and inverse problems. We show how this understanding can help to develop fast algorithms, explore underlying low dimensional structures, and analyze (in)stability of the underlying problem.

Find out more »### Yaiza Canzani – AMS 2021 Spring Sectional Meetings (Virtual)

Our assistant professor Yaiza Canzani is scheduled to speak at the AMS 2021 Spring Sectional Meetings (Virtual) on March 13 and 14. More details will be posted soon here: http://www.ams.org/meetings/sectional/2287_program_Unsched.html. Please attend if you are available!

Find out more »### Tsao-Hsien Chen, University of Minnesota – Geometric Methods in Representation Theory Seminar

Tsao-Hsien Chen, University of Minnesota Time: 4:00 pm, 03/19/21 Title: Towards derived Satake equivalence for symmetric varieties Abstract: In an ongoing project of D. Ben-Zvi, Y. Sakellaridis and A. Venkatesh, the authors propose a conjectural generalization of the derived Satake equivalence for complex reductive groups to spherical varieties. I will describe a program aimed at establishing their conjecture in the case of symmetric varieties (an important class of spherical varieties). A key ingredient is the relation between the Satake category for…

Find out more »### Nattalie Tamam, University of California at San Diego – Ergodic Theory Seminar

Nattalie Tamam, University of California at San Diego Title: Effective equidistribution of horospherical flows in infinite volume Abstract: Horospherical flows in homogeneous spaces have been studied intensively over the last several decades and have many surprising applications in various fields. Many basic results are under the assumption that the volume of the space is finite, which is crucial as many basic ergodic theorems fail in the setting of an infinite measure space.In the talk we will discuss the infinite volume…

Find out more »### Zhiwei Yun, MIT – Mathematics Colloquium

Zhiwei Yun, MIT Title: Conjugacy classes in the Weyl group and nilpotent orbits. Abstract: The Weyl group and the nilpotent orbits are two basic objects attached to a semisimple Lie group. The interplay between the two is a key ingredient in the classification of irreducible representations in various contexts. In this talk, I will describe two very different geometric constructions to relate these two objects, due to Kazhdan-Lusztig, Lusztig, and myself. The main result is that these two constructions give…

Find out more »### Dr. Bernat Font Garcia – Applied Mathematics Colloquium

Speaker: Dr. Bernat Font Garcia Position: Postdoctoral researcher at the Barcelona Supercomputing Center (BSC-CNS), formerly at University of Southampton (UK) Title: A ML model to simulate 3D turbulence in a 2D system applied to long cylindrical structures Abstract: Turbulence is a non-linear phenomenon in fluids involving a wide range of complex temporal and spatial structures. This often makes the resolution requirements of numerical simulations very high, yielding costly and time-consuming computations. Turbulence models are used to skip resolving a certain…

Find out more »### Alex Weekes, University of British Columbia – Geometric Methods in Representation Theory Seminar

Alex Weekes, University of British Columbia Title: Coulomb branches symmetrizable types Abstract: Braverman-Finkelberg-Nakajima have recently given a mathematical construction of the Coulomb branches for 3d N=4 theories. From a representation-theoretic perspective, one reason that their work is especially appealing is that affine Grassmannian slices of ADE types arise this way, associated to quiver gauge theories. By allowing general quivers, Coulomb branches also provide a candidate definition for affine Grassmannian slices in all symmetric Kac-Moody types. In this talk I will discuss joint work with Nakajima, where…

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