Spring School

Organizers: Polona Durcik, Joris Roos, and Andreas Seeger

The spring school will consist of lectures delivered by the participants. A typical participant will be a graduate student or postdoc and the total number of participants is limited to 15.

Every participant will submit preferences from a list of topics, most of them recent papers in the area. After being assigned to a paper, each participant will prepare a 50 min talk with a focus on the context and main ideas of the paper presented. Some longer papers may be assigned to two participants who should then coordinate their efforts. Selected participants may be asked to give a second 50 min talk during the week.

Participants must submit a 4-6 page summary of their assigned paper by May 1, 2024. The summaries will be compiled and made publicly available on this website. Further instructions for preparing the summaries will follow.

The spring school will take place in-person at UW Madison. Some very limited support is available for shared accommodations for non-local participants. 

If you would like to participate, please submit your application here as soon as possible and before January 28, 2024. (CLOSED)

• Schedule

• Proceedings

Topics

1. a. C. Muscalu, W. Schlag. Classical and Multilinear Harmonic Analysis, vol. 2. Chapter 2 (Paraproducts and the Coifman-Meyer theorem). Cambridge Studies in Advanced Mathematics, Cambridge University Press, 2013. 
   b. C. Muscalu, W. Schlag. Classical and Multilinear Harmonic Analysis, vol. 2. Chapter 4 (Calderon commutator). Cambridge Studies in Advanced Mathematics, Cambridge University Press, 2013.

2. M. Lacey, C. Thiele. Lp estimates for the bilinear Hilbert transform. Ann. Math (2) 146, no. 3, 693-724, 1997. (See also Chapter 6 of Muscalu-Schlag, vol. 2.)

3. C. Demeter, C. Thiele. On the two-dimensional bilinear Hilbert transform. Amer. J. Math. 132 (2010), no. 1, 201–256.

4. V. Kovač. Boundedness of the twisted paraproduct. Rev. Mat. Iberoam. 28 (2012), no. 4, 1143-1164.

5. V. Kovač, C. Thiele, P. Zorin-Kranich. Dyadic triangular Hilbert transform of two general and one not too general function. Forum of Mathematics, Sigma 3 (2015), e25.

6. a. X. Li. Bilinear Hilbert transforms along curves I: The monomial case. Anal. PDE 6 (2013), no. 1, 197-220.
   b. V. Lie. On the boundedness of the bilinear Hilbert transform along "non-flat" smooth curves. Amer. J. Math. 137 (2015), no. 2, 313-363.

7. M. Christ, P. Durcik, J. Roos. Trilinear smoothing inequalities and a variant of the triangular Hilbert transform. Adv. Math. 390 (2021), Paper No. 107863. (Also see M. Hsu, F. Y.-H. Lin, A. Stokolosa. A study guide for "Trilinear smoothing inequalities and a variant of the triangular Hilbert transform")

8. M. Christ. On trilinear oscillatory integral inequalities and related topics. arXiv, July 2020. 

9. M. Christ. On implicitly oscillatory quadrilinear integrals. arXiv, April 2022. (Also see M. Christ. A three term sublevel set inequality)

10. B. Hu, V. Lie. On the curved Trilinear Hilbert transform. arXiv, August 2023.

11. S. Peluse. On the polynomial Szemerédi theorem in finite fields. Duke Math. J. 168 (2019), no. 5, 749–774.

12. S. Peluse, S. Prendiville. Quantitative bounds in the non-linear Roth Theorem. arXiv, March 2019.

13. B. Krause, M. Mirek, T. Tao. Pointwise ergodic theorems for non-conventional bilinear polynomial averages. Ann. Math. 195, no. 3, 997-1109, 2022.

14. B. Krause, M. Mirek, S. Peluse,  J. Wright. Polynomial progressions in topological fields. arXiv, October 2022.

15. P. Durcik, J. Roos. A new proof of an inequality of Bourgain. To appear in Math. Res. Lett., 2022

16. B. Cook, A. Magyar, M. Pramanik. A Roth type theorem for dense subsets of Rd. Bull. London Math. Soc. 49, no. 4, 676-689, 2017.

17. Y. Do, R. Oberlin, E. Palsson.  Variation-norm and fluctuation estimates for ergodic bilinear averages. Indiana Univ. Math. J. 66 (2017), no. 1, 55-99

18. P. Durcik, V. Kovač, K. A. Škreb, C. Thiele. Norm variation of ergodic averages with respect to two commuting transformations. Ergodic Theory Dynam. Systems 39 (2019), no. 3, 658-688. 

19. M. Christ, Z. Zhou. A class of singular bilinear maximal functions. arXiv, March 2022.

Supported in part by grants from the National Science Foundation.