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Master of Science in Mathematics - Mathematical Finance | 2022 Geometric Analysis Conference
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Master of Science in Mathematics - Mathematical Finance | Department of Mathematics; Rutgers, The State University of New Jersey

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Master of Science in Mathematics - Mathematical Finance
2022 Geometric Analysis Conference

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Current Conference

  • Rutgers Gauge Theory, Low-Dimensional Topology, and Geometric Analysis Conference 2025

Next Year's Conference

  • Rutgers Gauge Theory, Low-Dimensional Topology, and Geometric Analysis Conference 2026

Past Conferences

  • Rutgers Gauge Theory, Low-Dimensional Topology, and Geometric Analysis Conference 2024
  • 2023 Geometric Analysis Conference
  • 2022 Geometric Analysis Conference
  • 2021 Geometric Analysis Conference
  • 2020 Geometric Analysis Conference
  • 2018 Geometric Analysis Conference
  • 2017 Geometric Analysis Conference
  • 2016 Geometric Analysis Conference

2022 Conference Schedule

  • Monday
  • Tuesday
  • Wednesday
  • Thursday

Coffee & Lunch Breaks

11:10 - 11:30 Coffee
12:30 - 2:00 Lunch
4:10 - 4:30 Coffee

Monday

Scalar Curvature: Structure and Regularity – Part 1/2

  • Speaker: Robin Neumayer
  • Time: 9:00-10:00
  • Abstract: A broad theme in geometric analysis aims to understand the geometric structure of Riemannian manifolds that satisfy constraints on curvature. Over the past 25 years, a rather complete picture has been given for the structure and a priori regularity of Riemannian manifolds with lower bounds on Ricci curvature, as well as their limit spaces. On the other hand, when one assumes only a lower bound on scalar curvature, the trace of the Ricci curvature, the situation is much less well understood. The scalar curvature asymptotically governs the volumes of balls of small radii, and arises in various settings in general relativity and differential geometry. This mini-course will focus on the structure and regularity of Riemannian manifolds with scalar curvature lower bounds.

 

Stable minimal hypersurfaces in 4-manifolds (Part 1/2)

  • Speaker: Chao Li
  • Time: 10:10-11:10
  • Abstract: Stable minimal surfaces in 3-manifolds have been extensively used to probe the topology of the ambient space. Important results include rigidity theorems in 3-manifolds with nonnegative Ricci or scalar curvature. In this minicourse, I will discuss how one may extend these results to stable minimal hypersurfaces in 4-manifolds. I will start with a few examples illustrating various non-rigidity phenomena and prove a rigidity theorem under the combination of sectional and scalar curvature conditions.

Hodge theory of almost complex 4-manifolds – Part 1/2

  • Speaker: Joana Cirici
  • Time: 11:20-12:20
  • Abstract: In this mini-course we will review the Hodge theory of compact complex surfaces from a new viewpoint: we will prove general properties for almost complex 4-manifolds, and observe how these collapse to well-known and strong properties the case of complex surfaces. Along the way, we will define Hodge numbers for arbitrary almost complex manifolds and will also discuss obstructions to integrability using Hodge and homotopy theory.

 

Scalar Curvature: Structure and Regularity – Part 2/2

  • Speaker: Robin Neumayer
  • Time: 2:00-3:00
  • Abstract: A broad theme in geometric analysis aims to understand the geometric structure of Riemannian manifolds that satisfy constraints on curvature. Over the past 25 years, a rather complete picture has been given for the structure and a priori regularity of Riemannian manifolds with lower bounds on Ricci curvature, as well as their limit spaces. On the other hand, when one assumes only a lower bound on scalar curvature, the trace of the Ricci curvature, the situation is much less well understood. The scalar curvature asymptotically governs the volumes of balls of small radii, and arises in various settings in general relativity and differential geometry. This mini-course will focus on the structure and regularity of Riemannian manifolds with scalar curvature lower bounds.

Stable minimal hypersurfaces in 4-manifolds (Part 2/2)

  • Speaker: Chao Li
  • Time: 3:10-4:10
  • Abstract: Stable minimal surfaces in 3-manifolds have been extensively used to probe the topology of the ambient space. Important results include rigidity theorems in 3-manifolds with nonnegative Ricci or scalar curvature. In this minicourse, I will discuss how one may extend these results to stable minimal hypersurfaces in 4-manifolds. I will start with a few examples illustrating various non-rigidity phenomena and prove a rigidity theorem under the combination of sectional and scalar curvature conditions.

Hodge theory of almost complex 4-manifolds – Part 2/2

  • Speaker: Joana Cirici
  • Time: 4:20-5:20
  • Abstract: In this mini-course we will review the Hodge theory of compact complex surfaces from a new viewpoint: we will prove general properties for almost complex 4-manifolds, and observe how these collapse to well-known and strong properties the case of complex surfaces. Along the way, we will define Hodge numbers for arbitrary almost complex manifolds and will also discuss obstructions to integrability using Hodge and homotopy theory.

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HillCenterMathematical Finance Master's Program
Department of Mathematics, Hill 348
Hill Center for Mathematical Sciences
Rutgers, The State University of New Jersey
110 Frelinghuysen Road
Piscataway, NJ 08854-8019

Email: finmath (at) math.rutgers.edu
Phone: +1.848.445.3920
Fax: +1.732.445.5530

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