Danyu YangPostdoctoral Research Fellow, Mathematical Institute, University of OxfordResearch Fellow and Tutor, Keble College, University of OxfordEmail:yangd "at" maths.ox.ac.uk Address:Mathematical Institute, University of Oxford Andrew Wiles Building, Radcliffe Observatory Quarter Woodstock Road, Oxford, OX2 6GG, UK |

**Education:**

2008-2012 Ph.D. in Mathematics (Clarendon Scholarship)

University of Oxford, Supervisor: Terry Lyons

Thesis: Partial sum process of orthogonal series as rough process

2004-2008 Bachelor degree in Mathematics (top 3%)

Fudan University, China

**Employment:**

2015-now Postdoctoral Research Fellow

Mathematical Institute, University of Oxford

2014-now Research Fellow and Tutor

Keble College, University of Oxford

2012-2015 Postdoctoral Research Fellow

Oxford-Man Institute, University of Oxford

**Research Interests:**

Rough Path Theory, Combinatorial Hopf Algebras, Stochastic Analysis and applications

**Publications:**

[1] The signature of a rough path: uniqueness (with H. Boedihardjo, X. Geng, T. Lyons)

[2] The theory of rough paths via one-forms and the extension of an argument of Schwartz to RDEs (with T. Lyons)

[3] Uniform factorial decay estimate for the remainder of rough Taylor expansion (with H. Boedihardjo, T. Lyons)

[4] Recovering the pathwise Itô solution from averaged Stratonovich solutions

*(with T. Lyons)* Electron. Commun. Probab., journal, (2015).

[5] Dimension-free Euler estimates of rough differential equations (with Y. Boutaib, L. G. Gyurkó, T. Lyons)

[6] G-Brownain motion as rough paths and differential equations driven by G-Brownian motion (with X. Geng, Z. Qian)

[7] The partial sum process of orthogonal expansions as geometric rough process with Fourier series as an example (with T. Lyons)

**Preprints:**

[1] Integration of geometric rough paths

Submitted for publication in Abel Symposia, Springer, arxiv, (2016).

[2] Integration of time-varying cocyclic one-forms against rough paths

*(with T. Lyons)* under revision, arxiv, (2016).

**Book in Progress:**

“The lecture notes for the theory of rough paths” (with H. Ni, T. Lyons)

World Scientific Publishing

**Selected Invited Talks:**

“Stochastic Analysis”, Durham Symposium, 10-20 July 2017.

“Workshop on BSDEs, SPDEs and their applications”, University of Edinburgh, 3-7 July

**2017.**“Integration of geometric rough paths”, Computation and Combinatorics in Dynamics Stochastics and Control, Abel Symposium, Norway, 2016.

“Integration of rough paths via one-forms”, Rough Paths, Regularity Structures and Related Topics, Oberwolfach Workshop, Germany, 2016.

**Invited Seminar/**

**Conference**

**Talks:**

"Integration of rough paths", Applied Algebra and Geometry, University of Edinburgh, 2017.

“Integration of geometric rough paths”, Young Researchers’ Forum, Fudan Univeristy, China, 2017.

“Integration of geometric rough paths”, Stochastic Analysis Seminar, Imperial College London, 2017.

“Integration of geometric rough paths”, Statistics for Differential Equations Driven by Rough Paths, Warwick, 2016.

“The theory of rough paths via one-forms”, Stochastic Analysis Seminar, University of Warwick, 2016.

“The theory of rough paths via one-forms”, Stochastic Analysis, Rough Paths, Geometry workshop, Imperial College, 2016.

“The theory of rough paths via one-forms”, Stochastic Processes and their Applications, contributed talk, Oxford, 2015.

“Integrating slow-varying linear one-forms against rough path”, Stochastic Analysis seminar, Oxford, 2014.

“RDE in Banach space and partial sum process of orthogonal series”, Workshop on Probability and its Applications, Oxford, 2014.

“Area operator and partial sum process”, TU Berlin, Germany, 2012.

“Partial sum process of orthogonal series as rough process”, University of Cambridge, 2011.

“The partial sum process of orthogonal expansion as geometric rough processes with Fourier series as an example”, Stochastic Analysis seminar, Oxford, 2011.

“Rough path, p-variation of a path from its lifted rough path”, Saint Flour, France, 2010.

“Maximum of a rough path from its signature”, IRTG SMCP summer school, Germany, 2009.

**Teaching:**

From Oct 2014, I am a Research Fellow and Tutor in Mathematics in Keble College in University of Oxford, responsible for the tutorials of multiple Prelims and Part A courses, to set and mark college examinations, to participate in undergraduate admissions, and to assist with the routine administration.

Prelims: Analysis, Multivariable Calculus, Constructive Mathematics

Part A: Probability, Metric Spaces and Complex Analysis, Numerical Analysis, Integration

Michaelmas 2014, Hilary 2016, Trinity 2016:

Lecturer (joint with Dr. Ni) of the Graduate course "Introduction to rough path theory" in Mathematical Institute.

Fellow of the Higher Education Academy, United Kingdom

Certificate in recognition of attainment against the UK Professional Standards Framework for teaching and learning support in higher education.

Recognition reference: PR095775 Date of Recognition: 10/11/2015.