# Richard Bamler

rbamler@berkeley.edu

## Topics Class on Ricci flow (Math 277)

I will be teaching a topics class on Ricci flow this fall semester (August 27-December 3, 2020).
The class will be taught over Zoom.
You are welcome to attend my class (even if you are not at UC Berkeley).
You can email me for the Zoom ID or click on the link below.

More information

## Research

R. Bamler, C. Cifarelli, R. Conlon, A. Deruelle, *"A new complete two-dimensional shrinking gradient Kähler-Ricci soliton"*, arxiv:2206.10785

R. Bamler, C. Li, C. Mantoulidis, *"Decomposing 4-manifolds with positive scalar curvature"*, arxiv:2206.09335

R. Bamler, P.-Y. Chan, Z. Ma, Y. Zhang, *"An optimal volume growth estimate for noncollapsed steady gradient Ricci solitons",* arXiv:2110.04661

R. Bamler, *"On the fundamental group of non-collapsed ancient Ricci flows",* arxiv:2110.02254

R. Bamler, B. Kleiner, *"Diffeomorphism groups of prime 3-manifolds",* arXiv:2108.03302

R. Bamler, *"Recent developments in Ricci flows",* Notices of the American Mathematical Society

R. Bamler, B. Chow, Y. Deng, Z. Ma, *"Four-Dimensional Steady Gradient Ricci Solitons with 3-Cylindrical Tangent Flows at Infinity",* arXiv:2102.04649, to appear in Advances in Mathematics

R. Bamler, *"Structure theory of non-collapsed limits of Ricci flows",* arxiv:2009.03243

R. Bamler, *"Compactness theory of the space of Super Ricci flows",* arxiv:2008.09298

R. Bamler, *"Entropy and heat kernel bounds on a Ricci flow background",* arxiv:2008.07093

R. Bamler, B. Kleiner, *"Ricci flow and contractibility of spaces of metrics"*, arxiv:1909.08710

R. Bamler, B. Kleiner, *"On the rotational symmetry of 3-dimensional κ-solutions"*, arxiv:1904.05388, Journal für die reine und angewandte Mathematik (Crelles Journal), vol. 2021, no. 779, 2021, pp. 37-55.

R. Bamler, B. Kleiner, *"Ricci flow and diffeomorphism groups of 3-manifolds"*, arXiv:1712.06197, to appear in JAMS

R. Bamler, B. Kleiner, *"Uniqueness and Stability of Ricci flow through singularities"*, arXiv:1709.04122, to appear in Acta Mathematica

R. Bamler, E. Cabezas-Rivas, B. Wilking, *"The Ricci flow under almost non-negative curvature conditions"*, arXiv:1707.03002, Invent. Math. 217 (2019), no. 1, 95-126

R. Bamler, *"Structure theory of singular spaces"*, arXiv:1603.05236, Journal of Functional Analysis, 272(6) (2017): 2504-2627 (article)

R. Bamler, *"Convergence of Ricci flows with bounded scalar curvature"*, arXiv:1603.05235, Annals of Mathematics 188, no. 3 (2018): 753-831

R. Bamler, *"Compactness properties of Ricci flows with bounded scalar curvature"*
arXiv:1512.08527, (old version, superseded by *Structure theory ...* and *Convergence of ...*)

R. Bamler, D. Maximo, *"Almost-rigidity and the extinction time of positively curved Ricci flows"*, arXiv:1506.03421, Math. Annalen 369 (2017), 899-911

R. Bamler, Q. Zhang, *"Heat kernel and curvature bounds in Ricci flows with bounded scalar curvature --- Part II"*, arXiv:1506.03154, Calc. Var. (2019) 58:49

R. Bamler, *"A Ricci flow proof of a result by Gromov on lower bounds for scalar curvature"*, arXiv:1505.00088, Math. Res. Letters, 23(2) (2016):325-337 (article)

R. Bamler, Q. Zhang, *"Heat kernel and curvature bounds in Ricci flows with bounded scalar curvature"*, arXiv:1501.01291, Advances in Mathematics, (2017), 319:396-450

R. Bamler, S. Brendle, *"A comparison principle for solutions to the Ricci flow"*, Math. Res. Letters, 22(4) (2015):983-988 (article)

R. Bamler, *"Long-time behavior of 3 dimensional Ricci flow -- Introduction"*, arXiv:1411.6658, Geometry & Topology 22-2 (2018), 757-774

R. Bamler, *"Long-time behavior of 3 dimensional Ricci flow -- A: Generalizations of Perelman's long-time estimates"*, arXiv:1411.6655, Geometry & Topology 22-2 (2018), 775-844

R. Bamler, *"Long-time behavior of 3 dimensional Ricci flow -- B: Evolution of the minimal area of simplicial complexes under Ricci flow"*, arXiv:1411.6649, Geometry & Topology 22-2 (2018), 845-892

R. Bamler, *"Long-time behavior of 3 dimensional Ricci flow -- C: 3-manifold topology and combinatorics of simplicial complexes in 3-manifolds"*, arXiv:1411.6647, Geometry & Topology 22-2 (2018), 893-948

R. Bamler, *"Long-time behavior of 3 dimensional Ricci flow -- D: Proof of the main results"*, arXiv:1411.6642, Geometry & Topology 22-2 (2018), 949-1068

R. Bamler, *"Long-time analysis of 3 dimensional Ricci flow III"*, arXiv:1310.4483 (2013), (old version, superseded by *Long-time behavior of 3 dimensional Ricci flow 0, A-D*)

R. Bamler, *"Long-time analysis of 3 dimensional Ricci flow II"*, arXiv:1112.5125 (2012), (old version, superseded by *Long-time behavior of 3 dimensional Ricci flow 0, A-D*)

R. Bamler, *"Long-time analysis of 3 dimensional Ricci flow I"*, arXiv:1112.5125 (2011), J. für reine und angewandte Mathematik, 725 (2017), 183-215

(as *"The long-time behavior of 3-dimensional Ricci flow on certain topologies"*)

R. Bamler, *"Stability of symmetric spaces of noncompact type under Ricci flow"* arXiv:1011.4267, Geom. Funct. Anal. 25 (2015), no. 2, 342–416.

R. Bamler, *"Stability of hyperbolic manifolds with cusps under Ricci flow"* arXiv:1004.2058, Adv. Math. 263 (2014), 412–467

R. Bamler, *"Construction of Einstein metrics by generalized Dehn filling"*, arXiv:0911.4730 (2009), Journal of the European Mathematical Society (JEMS) 14, 887-909 (2012) (link).

## Lecture Slides + Videos

Uniqueness of weak Ricci flows (talk 1, Bonn, 2017)

Classification of diffeomorphism groups of 3-manifolds through Ricci flow

Classification of diffeomorphism groups of 3-manifolds through Ricci flow (Beijing, May 2018)

Uniqueness of Weak Solutions to the Ricci flow and Topological Applications (Beijing, Zoom talk, May 2020)

Uniqueness of Weak Solutions to the Ricci flow and Topological Applications (MPI Leipzig, Zoom talk, June 2020)

Uniqueness of Weak Solutions to the Ricci flow and Topological Applications (Pacific Rim Conference, Zoom talk, August 2020) (recording)

Ricci flows in higher dimensions (Online Seminar on Geometric Analysis, August 2020; Virtual Workshop on Ricci and Scalar Curvature (recording)

Ricci flows in higher dimensions (Princeton, September 2020)

Uniqueness of Weak Solutions to the Ricci flow and Topological Applications (U Oregon, October 2020)

## Notes

R. Bamler, *"Ricci flow with surgery"*, diploma thesis (2007), (pdf)

## Seminar

Differential Geometry Seminar

## Teaching

Spring 2022: Math 140: Metric Differential Geometry

Spring 2022: Math 214: Differentiable Manifolds

Fall 2021: Math 16A: Analytic Geometry and Calculus

Spring 2021: Math 214: Differentiable Manifolds

Fall 2020: Math 16A: Analytic Geometry and Calculus

Spring 2021: Math 214: Differentiable Manifolds

Fall 2020: Math 277: Ricci flow

Fall 2020: Math 1A: Calculus

Fall 2018: Math 1A: Calculus

Fall 2018: Math 214: Differentiable Manifolds

Spring 2018: Math 1A: Calculus

Fall 2017: Math 140: Metric Differential Geometry

Spring 2017: Math 299: Geometric and analytic aspects of Ricci curvature

Fall 2016: Math 10A: Methods of Mathematics: Calculus, Statistics and Combinatorics

Fall 2015: Math 240: Riemannian Geometry

Fall 2015: Math 10A: Methods of Mathematics: Calculus, Statistics and Combinatorics

Spring 2015: Math 215B: Algebraic Topology II

Fall 2014: H110: Honors Linear Algebra

Winter 2014: Math 280: Ricci flow

Spring 2013: Math 51: Linear Algebra and Differential Calculus of Several Variables

Spring 2012: Math 175: Elementary Functional Analysis

Winter 2012: Math 172: Lebesgue Integration and Fourier Analysis