SCHEDULE OF TALKS

• 2:30 pm Tuesday, September 13th: Sangmin Park, Geometry of the Sliced Wasserstein Space

• 2:30 pm Tuesday, September 20th: Sangmin Park, Geometry of the Sliced Wasserstein Space

• 2:30 pm Tuesday, October 11th: Lantian Xu, Gradient flow based interacting particle methods for sampling, Slides

• 2:30 pm Tuesday, October 25th: Lantian Xu, Gradient flow based interacting particle methods for sampling

• 2:30 pm Tuesday, November 1st: Robert Pego, Multimarginal optimal transport and entropic regularization

• 2:30 pm Tuesday, November 8th: Robert Pego, Optimal transport model for mixing of incompressible fluids

• 2:30 pm Tuesday, November 15th: Xinjie He, Breaking the curse of dimension in multi-marginal optimal transport

• 2:30 pm Tuesday, November 22nd: Xinjie He, Breaking the curse of dimension in multi-marginal optimal transport

• 2:30 pm Tuesday, November 29th: TBA

• 2:30 pm Tuesday, December 6th: TBA

REFERENCES

• Helgason, S. (2010). Integral Geometry and Radon Transforms, Chapter 1

• Bonnotte, N. (2013). Unidimensional and Evolution Methods for Optimal Transportation, Chapter 5 of PhD Thesis

• Lu, J., Lu, Y., & Nolen, J. (2019). Scaling limit of the Stein variational gradient descent: The mean field regime. SIAM Journal on Mathematical Analysis, 51(2), 648-671.

• Carrillo, J. A., Craig, K., & Patacchini, F. S. (2019). A blob method for diffusion. Calculus of Variations and Partial Differential Equations, 58(2), 1-53.

• Liu, Q., & Wang, D. (2016). Stein variational gradient descent: A general purpose bayesian inference algorithm. Advances in neural information processing systems, 29.

• Arbel, M., Korba, A., Salim, A., & Gretton, A. (2019). Maximum mean discrepancy gradient flow. Advances in Neural Information Processing Systems, 32.

• Gong, W., Li, Y., & Hernández-Lobato, J. M. (2020). Sliced kernelized Stein discrepancy. arXiv preprint arXiv:2006.16531.

• Luca Nenna (2016). Numerical methods for multi-marginal optimal transportation. PhD Thesis.

• Benamou, JD., Carlier, G. & Nenna, L. Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithm. Numer. Math. 142, 33–54 (2019). Link

• Liu, JG., Pego, R.L. & Slepčev, D. Least action principles for incompressible flows and geodesics between shapes. Calc. Var. 58, 179 (2019). Link

• Friesecke, G., Vögler, D. (2018). Breaking the curse of dimension in multi-marginal Kantorovich Optimal Transport on finite state spaces. SIAM J. Math. Anal. 50(4), 3996-4019. Link