SUMMER SCHOOL
Paraproducts and Analysis of Rough Paths
15 Basics
69 The signature
1013 Applications
1416 Paraproducts and rough paths

Differential equations driven by rough paths: an approach via discrete approximation.
by A. Davie
Appl. Math. Res. Express. AMRX 2007, no. 2, Art. ID abm009, 40 pp
(2007)
[presenter: Yujia Zhai]

Controlling rough paths. Part I
by M. Gubinelli
J. Funct. Anal. 216 (2004), no. 1, 86140.
[presenter: Cristina Benea]

Controlling rough paths. Part II
by M. Gubinelli
J. Funct. Anal. 216 (2004), no. 1, 86140.
[presenter: Gianmarco Brocchi]

Ramification of rough paths.
by M. Gubinelli
J. Differential Equations 248 (2010), no. 4, 693721.
[presenter: Robert Crowell]

Integrability and tail estimates for Gaussian rough differential equations.
by T. Cass, C. Litterer, and T. Lyons
Ann. Probab. 41 (2013), no. 4, 30263050.
[presenter: Luigi Borasi]

Inverting the signature of a path
by T. Lyons, W. Xu
arXiv:1406.7833
[presenter: Joao Ramos]

Characteristic functions of measures on geometric rough paths.
by I. Chevyrev and T. Lyons
arXiv:1307.3580
.
[presenter: Michal Warchalski]

Decay Rate of Iterated Integrals of Branched Rough Paths
by H. Boedihardjo
arXiv:1501.05641
.
[presenter: Marco Fraccaroli ]

Physical Brownian motion in magnetic field as rough path
by P. Friz, P. Gassiat, T. Lyons
Trans. Amer. Math. Soc. 367 (2015), no. 11, 79397955.
[presenter: Kevin O'Neill]

Reflected rough differential equations.
by A. Shigeki
Stochastic Process. Appl. 125 (2015), no. 9, 3570–3595.
Skip section 5 if time runs out.
[presenter: Joris Roos]

Rough solutions for the periodic Korteweg–de Vries equation.
by M. Gubinelli
Commun. Pure Appl. Anal. 11 (2012), no. 2, 709733.
[presenter: Jonas Jansen ]

Deterministic homogenization for fastslow systems with chaotic noise
by D. Kelly and I. Melbourne
arXiv:1409.5748
.
[presenter: Johanna Richter]

A signed measure on rough paths associated to a PDE of high order: results and conjectures.
by D. Levin and T. Lyons
Rev. Mat. Iberoam. 25 (2009), no. 3, 971994.
[presenter: Gennady Uraltsev]

The partial sum process of orthogonal expansions as geometric rough process with Fourier series as an example—an improvement of MenshovRademacher theorem.
by T. Lyons and D. Yang
J. Funct. Anal. 265 (2013), no. 12, 30673103.
Put less emphasis on Fourier series, if time runs out.
[presenter: Dominique Maldague]

Paracontrolled distributions and singular PDEs.
by M. Gubinelli, P. Imkeller, N. Perkowski
Forum Math. Pi 3 (2015), e6, 75 pp.
Do RDE, skip Burgers and PAM.
[presenter: Immanual Zachhuber]

The NashMoser theorem and paradifferential operators.
by L. Hörmander
Analysis, et cetera, 429449, Academic Press, Boston, MA, 1990.
[presenter: Polona Durcik]

Geometric versus NonGeometric Rough Paths.
by M. Hairer, D. Kelly
Annales de l'Institut Henri Poincare, Probabilites et Statistiques
51, no. 1 (February
2015): 207{51. doi:10.1214/13AIHP564 Analysis, et cetera, 429449, Academic Press, Boston, MA, 1990.
Do theorem 1.9, skip sections 3 and 5.
[presenter: Nikolay Barashkov]

Quasilinear SPDE via rough paths.
by F. Otto, and H. Weber
Preprint,
arXiv:1605.09744
.
[presenter: Pavel ZorinKranich]

The continuous Anderson hamiltonian in dimension two
by R. Allez and K. Chouk
Preprint,
arXiv:1511.02718
.
[presenter: Irina Holmes]