Beca doctoral FPI en la UAM

Name of the project: Arithmetic Combinatorics and Analysis

Summary: This PhD project, to be carried out at the Autonomous University of Madrid (UAM), evolves at the interface between analysis and combinatorics, and offers various possible lines of research, especially within the broad area of arithmetic combinatorics and its ramifications in analysis. Possible topics include the following:

• higher-order Fourier analysis, its theoretical development (particularly in connection with the rapidly growing theory of nilspaces) as well as its recent quantitative or algorithmic progress.

• questions in ergodic theory related to higher-order Fourier analysis or to arithmetic and combinatorial problems (e.g. the structural analysis of Host-Kra factors and its applications, connections between ergodic theory and tiling or packing questions, Motzkin’s problem, etc.)

• questions in arithmetic combinatorics (e.g. the 3k-4 problem in cyclic groups of prime order, applications of entropy in arithmetic combinatorics, quantitative quadratic Fourier analysis and its number-theoretic applications, and miscellaneous other questions).

PI: Pablo Candela (pablo.candela@icmat.es). Any interested potential candidate is welcome to contact the advisor directly at their earliest convenience, to obtain more information on the PhD program at the UAM and on the application process, which is expected to begin in November 2025.

Candidate’s Profile: The PhD researcher is expected to work on topics in the aforementioned directions. The interested candidates are encouraged to discuss more specific topics informally with the PhD advisor soon, prior to their formal application to the PhD program.

Deadline: TBD

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