Papers / PreprintsMitch Taylor2024-03-24T01:02:12+00:00 GRADUATE RESEARCH SHARP WELL-POSEDNESS FOR THE FREE BOUNDARY MHD EQUATIONS, with M. Ifrim, B. Pineau and D. Tataru. January 1, 2025 COORDINATE SYSTEMS IN BANACH SPACES AND LATTICES, with A. Avilés, C. Rosendal and P. Tradacete. June 27, 2024 BANACH LATTICES WITH UPPER p-ESTIMATES: FREE AND INJECTIVE OBJECTS, with E. García-Sánchez, D. H. Leung and P. Tradacete, Math Ann. March 1, 2024 LOW REGULARITY SOLUTIONS FOR THE GENERAL QUASILINEAR ULTRAHYPERBOLIC SCHRÖDINGER EQUATION, with B. Pineau, ARMA. November 9, 2023 SHARP HADAMARD LOCAL WELL-POSEDNESS, ENHANCED UNIQUENESS AND POINTWISE CONTINUATION CRITERION FOR THE INCOMPRESSIBLE FREE BOUNDARY EULER EQUATIONS, with M. Ifrim, B. Pineau and D. Tataru. September 20, 2023 STABLE PHASE RETRIEVAL IN FUNCTION SPACES, with D. Freeman, B. Pineau and T. Oikhberg, Math. Ann. October 20, 2022 FREE BANACH LATTICES with T. Oikhberg, P. Tradacete and V.G. Troitsky, J. Eur. Math. Soc. (JEMS). October 20, 2022 EXAMPLES OF HÖLDER-STABLE PHASE RETRIEVAL, with M. Christ and B. Pineau, Math. Res. Lett. May 25, 2022 GLOBAL WELL-POSEDNESS FOR THE GENERALIZED DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION, with B. Pineau. December 10, 2021 NO PURE CAPILLARY SOLITARY WAVES EXIST IN 2D FINITE DEPTH, with M. Ifrim, B. Pineau and D. Tataru, SIAM J. Math. Anal., Vol. 54, No. 4, p. 4452-4464, 2022. April 24, 2021 FREE BANACH LATTICES UNDER CONVEXITY CONDITIONS, with H.J. Sanchez, N.J Laustsen, P. Tradacete and V.G. Troitsky, RACSAM 116 (2022), No. 1, Paper No. 15, 25 p. March 13, 2021 A SCHAUDER BASIS FOR L2 CONSISTING OF NON-NEGATIVE FUNCTIONS, with D. Freeman and A.M. Powell, Math. Ann., 381, 181-208 (2021). March 21, 2020 BIBASIC SEQUENCES IN BANACH LATTICES, with V.G. Troitsky, J. Funct. Anal., 278 (2020), no. 10, 108448, 33 pp. August 26, 2019 COMPLETENESS OF UNBOUNDED CONVERGENCES, Proc. Amer. Math. Soc., 146 (2018) 3413 – 3423. November 1, 2017 METRIZABILITY OF MINIMAL AND UNBOUNDED TOPOLOGIES, with M. Kandić, J. Math. Anal. Appl., 466 (2018), no.1, 144-159. September 14, 2017 UNBOUNDED TOPOLOGIES AND UO-CONVERGENCE IN LOCALLY SOLID VECTOR LATTICES, J. Math. Anal. Appl., 472 (2019), no.1, 981-1000. August 28, 2017 UNDERGRADUATE RESEARCH NOTE ON UNIQUENESS OF THE ISOTROPIC SOLUTION OF THE 2D DOI-ONSAGER MODEL, with X. Yu. December 5, 2017 UNBOUNDED CONVERGENCES IN VECTOR LATTICES December 10, 2021 A COLLECTION OF RESULTS ON NONLINEAR DISPERSIVE EQUATIONS, BANACH LATTICES AND PHASE RETRIEVAL September 20, 2023 RESEARCH VISTS, CONFERENCES AND SEMINAR TALKS Unbounded topologies and uo-convergence in locally solid vector lattices, Positivity IX, University of Alberta, Edmonton, Canada, July 17-21, 2017. August 28, 2017 Schauder bases with order convergent partial sums, Banach spaces seminar, Texas A&M University, February 23, 2018. December 20, 2018 Unbounded topologies with a view towards Banach lattices, Recent Advances in Banach Lattices, CMO/BIRS, Oaxaca, Mexico, April 29-May 4, 2018, video lecture. December 20, 2018 Two talks at the Probabilistic Operator Algebra Seminar, UC Berkeley. December 20, 2018 Minimal topologies on vector lattices, Recent Advances in Functional Analysis, Kent State University, October 11-14, 2018, poster. December 20, 2018 Duke University, February 10-19, 2019, research with Dan Freeman. Second visit to Durham August 12-20, 2022. February 23, 2019 Four visits to ICMAT (Madrid), including a talk at the Workshop on Banach spaces and Banach lattices I (minimal topologies), a plenary talk at the Workshop on Banach spaces and Banach lattices II (free Banach lattices), and two talks at the analysis seminar (bibases and phase retrieval). Additional visit to Murcia May 2022 and participation in the Workshop on Geometric Valuation Theory — from convex sets to functions, CIEM, Castro-Urdiales, June 2023. October 21, 2022 Semester at MSRI, Spring 2021. October 21, 2022 Four talks at the Harmonic Analysis and Differential Equations Seminar (HADES), Berkeley. October 21, 2022 Stable phase retrieval in function spaces, ETH Zurich, October 12, 2022. October 21, 2022 Chicago, July 2021, Research with Timur Oikhberg. October 21, 2022 Extending topologies to the universal sigma-completion of a vector lattice, Positivity X, Pretoria, July 8-12, 2019. October 21, 2022 Free Banach lattices: Subspace structure and basic sequences, Banach spaces webinar, October 16, 2020. October 21, 2022 The subspace structure of free Banach lattices, Positivity Webinar, April 1, 2021. October 21, 2022 Graduate student fluid dynamics workshops at MSRI (2020) and Oberwolfach (2022). October 21, 2022 Stable phase retrieval in function spaces, Recent advances in Banach lattices, BIRS, May 7-12, 2023. October 21, 2022 No pure capillary solitary waves exist in 2D, Recent Advances in Mathematical Fluid Dynamics, Duke University, May 20-24. November 9, 2023 Instructor for the ICMAT-IMAG DOC-COURSE IN FUNCTIONAL ANALYSIS, Spain, June 12-30, 2023. November 9, 2023 SLMath, Mathematical Problems in Fluid Dynamics, part 2, July 17-Aug. 11, 2023. November 9, 2023 Low regularity well-posedness for the general quasilinear Schrödinger equation, Analysis seminar, ETH Zürich, Oct. 24, 2023. November 9, 2023 Stable phase retrieval in function spaces, Cambridge University, Nov. 1, 2023. Additional stay in Peterhouse college Oct. 31-Nov. 3 and Trinity college Nov. 3-7. November 9, 2023 Stable phase retrieval in function spaces, Part II, Banach space webinar, Feb. 17, 2023. November 9, 2023 Stable phase retrieval in function spaces, CodEx webinar, July 11, 2023. November 9, 2023 Low regularity solutions to the general quasilinear Schrödinger equation at the Oberwolfach Seminar: Scattering Resonances in Quantum Mechanics, General Relativity and Hyperbolic Dynamics, Nov. 19-24, 2023. November 9, 2023 Host for N. Laustsen and T. Oikhberg, May 3-7 and A. Aviles and P. Tradacete, May 12-17, Alberta, 2023. November 9, 2023 Host for B. Pineau, Nov. 10-19 and D. Freeman, Nov. 27-Dec. 3, ETH Zürich, 2023. November 9, 2023 Co-organizer of the workshop Lattice Structures in Analysis, May 6-30, ICMAT, Madrid, 2024. November 9, 2023 Sharp well-posedness for the free boundary Euler equations, Cambridge PDE seminar, Feb. 26, 2024. March 1, 2024 Stable phase retrieval in function spaces, EPFL number theory seminar, Mar. 26, 2024. March 24, 2024 On the dynamics of the free boundary Euler equations, ETH Zurich symposium on PDE and Mathematical Physics, April 23, 2024. April 19, 2024 Sharp Hadamard well-posedness for the incompressible free boundary Euler equations, PDEs and Fluid Mechanics seminar, ICMAT, May 22, 2024. May 26, 2024 Stable phase retrieval in function spaces, Stobl24, June 9-15, 2024. Visit to the Acoustics Research Institute and University of Vienna, June 15-20, 2024. May 26, 2024 Phase retrieval in mathematics and applications, Lorentz center, August 5-9, 2024. August 14, 2024 Free Banach lattices, International workshop on operator theory and applications (IWOTA), August 12-16, University of Kent, Canterbury, 2024. August 14, 2024 Host for Pedro Tradacete, ETH Zurich, August 19-25, 2024. October 14, 2024 The nonlinear Fourier transform for better than square summable, Oberwolfach: Quantum signal processing and nonlinear Fourier analysis, Oct. 6-11, 2024. October 14, 2024 Host for Joao Ramos, ETH Zurich, Nov. 21-Dec. 1, 2024. November 23, 2024 Almost everywhere convergence of series and descriptive set theory, hosted by Tomasz Kania, Jagiellonian University, Poland, Dec. 1-6, 2024. November 23, 2024 Stable phase retrieval in function spaces, hosted by Vladimir Troitsky, University of Alberta, Canada, Jan. 20-24, 2025. March 9, 2025 Host for Joao Ramos, ETH Zurich, Feb. 1-7, 2025. March 9, 2025 Stable phase retrieval, Seminário de Análise e Equações Diferenciais, Lisbon, Portugal, hosted by Joao Ramos, Feb. 11-15, 2025. March 9, 2025 Host for Ben Pineau, ETH Zurich, Feb. 20-23 and March 1-4, 2025. March 9, 2025 Sharp well-posedness for the free boundary Euler equations, Conference on Mathematics of Wave Phenomena, Karlsruhe, Germany, Feb. 24-28, 2025. March 9, 2025 Stable phase retrieval in function spaces, ETH Zurich Analysis seminar, March 4, 2025. March 9, 2025 Almost everywhere convergence of series and descriptive set theory, ICMAT Madrid, hosted by Pedro Tradacete, March 10-15, 2025. March 9, 2025 Sharp well-posedness for the free boundary MHD equations, PDE and Mathematical Physics seminar, ETH Zurich and UZH, March 27, 2025. March 9, 2025 Archives Archives Select Month March 2025 (8) January 2025 (1) November 2024 (2) October 2024 (2) August 2024 (2) June 2024 (1) May 2024 (2) April 2024 (1) March 2024 (3) November 2023 (12) September 2023 (2) October 2022 (12) May 2022 (1) December 2021 (2) April 2021 (1) March 2021 (1) March 2020 (1) August 2019 (1) February 2019 (1) December 2018 (4) December 2017 (1) November 2017 (1) September 2017 (1) August 2017 (2) Filter CategoriesFilter Categories Select Category Masters Research (16) Talks (46) Undergraduate Research and Theses (3)
SHARP WELL-POSEDNESS FOR THE FREE BOUNDARY MHD EQUATIONS, with M. Ifrim, B. Pineau and D. Tataru. January 1, 2025
COORDINATE SYSTEMS IN BANACH SPACES AND LATTICES, with A. Avilés, C. Rosendal and P. Tradacete. June 27, 2024
BANACH LATTICES WITH UPPER p-ESTIMATES: FREE AND INJECTIVE OBJECTS, with E. García-Sánchez, D. H. Leung and P. Tradacete, Math Ann. March 1, 2024
LOW REGULARITY SOLUTIONS FOR THE GENERAL QUASILINEAR ULTRAHYPERBOLIC SCHRÖDINGER EQUATION, with B. Pineau, ARMA. November 9, 2023
SHARP HADAMARD LOCAL WELL-POSEDNESS, ENHANCED UNIQUENESS AND POINTWISE CONTINUATION CRITERION FOR THE INCOMPRESSIBLE FREE BOUNDARY EULER EQUATIONS, with M. Ifrim, B. Pineau and D. Tataru. September 20, 2023
STABLE PHASE RETRIEVAL IN FUNCTION SPACES, with D. Freeman, B. Pineau and T. Oikhberg, Math. Ann. October 20, 2022
FREE BANACH LATTICES with T. Oikhberg, P. Tradacete and V.G. Troitsky, J. Eur. Math. Soc. (JEMS). October 20, 2022
EXAMPLES OF HÖLDER-STABLE PHASE RETRIEVAL, with M. Christ and B. Pineau, Math. Res. Lett. May 25, 2022
GLOBAL WELL-POSEDNESS FOR THE GENERALIZED DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION, with B. Pineau. December 10, 2021
NO PURE CAPILLARY SOLITARY WAVES EXIST IN 2D FINITE DEPTH, with M. Ifrim, B. Pineau and D. Tataru, SIAM J. Math. Anal., Vol. 54, No. 4, p. 4452-4464, 2022. April 24, 2021
FREE BANACH LATTICES UNDER CONVEXITY CONDITIONS, with H.J. Sanchez, N.J Laustsen, P. Tradacete and V.G. Troitsky, RACSAM 116 (2022), No. 1, Paper No. 15, 25 p. March 13, 2021
A SCHAUDER BASIS FOR L2 CONSISTING OF NON-NEGATIVE FUNCTIONS, with D. Freeman and A.M. Powell, Math. Ann., 381, 181-208 (2021). March 21, 2020
BIBASIC SEQUENCES IN BANACH LATTICES, with V.G. Troitsky, J. Funct. Anal., 278 (2020), no. 10, 108448, 33 pp. August 26, 2019
COMPLETENESS OF UNBOUNDED CONVERGENCES, Proc. Amer. Math. Soc., 146 (2018) 3413 – 3423. November 1, 2017
METRIZABILITY OF MINIMAL AND UNBOUNDED TOPOLOGIES, with M. Kandić, J. Math. Anal. Appl., 466 (2018), no.1, 144-159. September 14, 2017
UNBOUNDED TOPOLOGIES AND UO-CONVERGENCE IN LOCALLY SOLID VECTOR LATTICES, J. Math. Anal. Appl., 472 (2019), no.1, 981-1000. August 28, 2017
NOTE ON UNIQUENESS OF THE ISOTROPIC SOLUTION OF THE 2D DOI-ONSAGER MODEL, with X. Yu. December 5, 2017
A COLLECTION OF RESULTS ON NONLINEAR DISPERSIVE EQUATIONS, BANACH LATTICES AND PHASE RETRIEVAL September 20, 2023
Unbounded topologies and uo-convergence in locally solid vector lattices, Positivity IX, University of Alberta, Edmonton, Canada, July 17-21, 2017. August 28, 2017
Schauder bases with order convergent partial sums, Banach spaces seminar, Texas A&M University, February 23, 2018. December 20, 2018
Unbounded topologies with a view towards Banach lattices, Recent Advances in Banach Lattices, CMO/BIRS, Oaxaca, Mexico, April 29-May 4, 2018, video lecture. December 20, 2018
Minimal topologies on vector lattices, Recent Advances in Functional Analysis, Kent State University, October 11-14, 2018, poster. December 20, 2018
Duke University, February 10-19, 2019, research with Dan Freeman. Second visit to Durham August 12-20, 2022. February 23, 2019
Four visits to ICMAT (Madrid), including a talk at the Workshop on Banach spaces and Banach lattices I (minimal topologies), a plenary talk at the Workshop on Banach spaces and Banach lattices II (free Banach lattices), and two talks at the analysis seminar (bibases and phase retrieval). Additional visit to Murcia May 2022 and participation in the Workshop on Geometric Valuation Theory — from convex sets to functions, CIEM, Castro-Urdiales, June 2023. October 21, 2022
Four talks at the Harmonic Analysis and Differential Equations Seminar (HADES), Berkeley. October 21, 2022
Extending topologies to the universal sigma-completion of a vector lattice, Positivity X, Pretoria, July 8-12, 2019. October 21, 2022
Free Banach lattices: Subspace structure and basic sequences, Banach spaces webinar, October 16, 2020. October 21, 2022
Stable phase retrieval in function spaces, Recent advances in Banach lattices, BIRS, May 7-12, 2023. October 21, 2022
No pure capillary solitary waves exist in 2D, Recent Advances in Mathematical Fluid Dynamics, Duke University, May 20-24. November 9, 2023
Instructor for the ICMAT-IMAG DOC-COURSE IN FUNCTIONAL ANALYSIS, Spain, June 12-30, 2023. November 9, 2023
Low regularity well-posedness for the general quasilinear Schrödinger equation, Analysis seminar, ETH Zürich, Oct. 24, 2023. November 9, 2023
Stable phase retrieval in function spaces, Cambridge University, Nov. 1, 2023. Additional stay in Peterhouse college Oct. 31-Nov. 3 and Trinity college Nov. 3-7. November 9, 2023
Stable phase retrieval in function spaces, Part II, Banach space webinar, Feb. 17, 2023. November 9, 2023
Low regularity solutions to the general quasilinear Schrödinger equation at the Oberwolfach Seminar: Scattering Resonances in Quantum Mechanics, General Relativity and Hyperbolic Dynamics, Nov. 19-24, 2023. November 9, 2023
Host for N. Laustsen and T. Oikhberg, May 3-7 and A. Aviles and P. Tradacete, May 12-17, Alberta, 2023. November 9, 2023
Co-organizer of the workshop Lattice Structures in Analysis, May 6-30, ICMAT, Madrid, 2024. November 9, 2023
Sharp well-posedness for the free boundary Euler equations, Cambridge PDE seminar, Feb. 26, 2024. March 1, 2024
On the dynamics of the free boundary Euler equations, ETH Zurich symposium on PDE and Mathematical Physics, April 23, 2024. April 19, 2024
Sharp Hadamard well-posedness for the incompressible free boundary Euler equations, PDEs and Fluid Mechanics seminar, ICMAT, May 22, 2024. May 26, 2024
Stable phase retrieval in function spaces, Stobl24, June 9-15, 2024. Visit to the Acoustics Research Institute and University of Vienna, June 15-20, 2024. May 26, 2024
Free Banach lattices, International workshop on operator theory and applications (IWOTA), August 12-16, University of Kent, Canterbury, 2024. August 14, 2024
The nonlinear Fourier transform for better than square summable, Oberwolfach: Quantum signal processing and nonlinear Fourier analysis, Oct. 6-11, 2024. October 14, 2024
Almost everywhere convergence of series and descriptive set theory, hosted by Tomasz Kania, Jagiellonian University, Poland, Dec. 1-6, 2024. November 23, 2024
Stable phase retrieval in function spaces, hosted by Vladimir Troitsky, University of Alberta, Canada, Jan. 20-24, 2025. March 9, 2025
Stable phase retrieval, Seminário de Análise e Equações Diferenciais, Lisbon, Portugal, hosted by Joao Ramos, Feb. 11-15, 2025. March 9, 2025
Sharp well-posedness for the free boundary Euler equations, Conference on Mathematics of Wave Phenomena, Karlsruhe, Germany, Feb. 24-28, 2025. March 9, 2025
Almost everywhere convergence of series and descriptive set theory, ICMAT Madrid, hosted by Pedro Tradacete, March 10-15, 2025. March 9, 2025
Sharp well-posedness for the free boundary MHD equations, PDE and Mathematical Physics seminar, ETH Zurich and UZH, March 27, 2025. March 9, 2025