Dr Daniele Semola

Status

Postdoctoral Research Associate

Research groups

Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Recent books

Preface Ambrosio, L Brué, E Semola, D (01 Jan 2021)

Lectures on Optimal Transport Ambrosio, L Brué, E Semola, D (01 Jan 2021)

Teaching

Regularity Theory of Spaces with lower Ricci curvature bounds. 2022.

Research interests

My main research topic are non smooth spaces with lower curvature bounds, at the interface between Analysis and Geometry.

Mainly I am interested on the study of geometric and functional inequalities on these spaces and on their fine structure.

Recent publications

Rectifiability of the reduced boundary for sets of finite perimeter over RCD(K,N) spaces

Bruè, E Pasqualetto, E Semola, D Journal of the European Mathematical Society (15 Feb 2022)

Boundary regularity and stability for spaces with Ricci bounded below

Bruè, E Naber, A Semola, D Inventiones Mathematicae volume 228 777-891 (11 Feb 2022)

Improved regularity estimates for Lagrangian flows on RCD(K, N) spaces

Bruè, E Deng, Q Semola, D Nonlinear Analysis: Theory Methods and Applications volume 214 (08 Oct 2021)

Rectifiability of RCD(K,N) spaces via δ-splitting maps

Brue, E Pasqualetto, E Semola, D Annales Fennici Mathematici volume 46 issue 1 465-482 (21 Jun 2021)

The equality case in Cheeger's and Buser's inequalities on
$\mathsf{RCD}$ spaces

Ponti, N Mondino, A Semola, D Journal of Functional Analysis

Prizes, awards, and scholarships

Benedetto Sciarra Prize of the Scuola Normale Superiore of Pisa (2019).

Gioacchino Iapichino Prize of the Accademia Nazionale dei Lincei (2022).

Major / recent publications

E. Bruè, D. Semola, Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows, Comm. Pure Appl. Math., 73: 1141-1204, doi:10.1002/cpa.21849.

L. Ambrosio, E. Bruè, D. Semola, Rigidity of the 1-Bakry-Émery inequality and sets of finite perimeter in RCD spaces, Geom. Funct. Anal. 29 (2019), no. 4, 949–1001.

E. Bruè, A. Naber, D. Semola, Boundary regularity and stability for spaces with Ricci bounded below, Invent. Math. 228 (2022), no. 2, 777–891.

E. Bruè, E. Pasqualetto, D. Semola, Rectifiability of the reduced boundary for sets of finite perimeter over RCD(K,N) spaces, Journal of the European Mathematical Society (2022).