Philippe Michel

philippe.michel@epfl.ch +41 21 693 25 76 http://tan.epfl.ch/philippe.michel

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Biography Awards Publications Teaching & PhD

Ph. Michel's main research interest lie in the field of analytic number theory and range over a variety of techniques and methods which include: arithmetic geometry, exponential sums, sieve methods, automorphic forms and allied representations, L-functions and more recently ergodic theory. Ph. Michel is a former student of ENS Cachan and obtained his PhD in Universté Paris XI in 1995 under the guidance of E. Fouvry. From 1995 to 1998 he was maître de conférence at Universté Paris XI and full professor at Université Montpellier II until 2008 then when he joined EPFL. Ph. Michel was awarded the Peccot-Vimont prize, has been member of the Institut Universitaire de France and wa invited speaker at the 2006 International Congress of Mathematician.

Awards

Peccot-Vimont prize

CollÃ¨ge de France

1999

member of the Academia Europaea (Academy of Europe) since 2011 and Fellow of the American Math. Society since 2012. ERC Advanced Grant

Infoscience

Toroidal families and averages of L-functions, I

E. Fouvry; E. Kowalski; P. Michel

Acta Arithmetica. 2024. DOI : 10.4064/aa230323-24-5.

Philippe Michel

Awards

Infoscience

Toroidal families and averages of L-functions, I

The unipotent mixing conjecture

On algebraic twists with composite moduli

ALGEBRAIC TWISTS OF GL3 x GL2 L-FUNCTIONS

Algebraic twists of GL(2) automorphic forms

Simultaneous supersingular reductions of CM elliptic curves

Recent Progresses On The Subconvexity Problem

Some recents advances on Duke’s equidistribution theorems

Moments of L-functions and exponential sums

Bilinear forms with Kloosterman sums and applications

On Moments Of Twisted L-Functions

On Short Sums Of Trace Functions

Some applications of smooth bilinear forms with Kloosterman sums

Analytic twists of modular forms and applications

Large Sieve Inequalities for Algebraic Trace Functions

On The Exponent Of Distribution Of The Ternary Divisor Function

A study in sums of products

Algebraic twists of modular forms and Hecke orbits

Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions

Algebraic Trace Functions Over The Primes

An inverse theorem for Gowers norms of trace functions over F-p

Hybrid Bounds For Automorphic Forms On Ellipsoids Over Number Fields

Problème de sous-convexité pour GL2xGL1

Counting Sheaves Using Spherical Codes

Sup-norms of Eigenfunctions on Arithmetic Ellipsoids

Distribution of periodic torus orbits and Duke's theorem for cubic fields

The Subconvexity Problem For Gl(2)

The distribution of periodic torus orbits on homogeneous spaces

Some effective results for $\times a \times b$

Analytic number theory and families of automorphic L-functions

Heegner points and non-vanishing of Rankin/Selberg $L$-functions.

Bounds for modular $L$-functions in the level aspect

On the sign change of Kloosterman sums. (Sur le changement de signe des sommes de Kloosterman.)

A Burgess-like subconvex bound for twisted $L$-functions (Appendix 2 by Z. Mao).

Equidistribution, $L$-functions and ergodic theory: on some problems of Yu. Linnik.

The subconvexity problem for Rankin-Selberg $L$-functions and equidistribution of Heegner points. II

Equidistribution, L-functions and Ergodic Theory: on some problems of Y.V Linnik

On the complex moments of symmetric power $L$-functions at $s = 1$

Pseudorandomness of the sign of Kloosterman's sums

The subconvexity problem for Rankin-Selberg $L$-functions and equidistribution of Heegner points

Families of $L$-functions of automorphic forms and applications. (Familles de fonctions $L$ de formes automorphes et applications.)

On the Shifted Convolution Problem

Horizontal vs. Vertical SATO/TATE

Sums of moduli of exponential sums. (Sommes de modules de sommes d'exponentielles.)

Asymptotic sieve and Kloosterman sums. (Crible asymptotique et sommes de Kloosterman)

Random Matrix Theory and the distribution of zeros of $L$-functions. (Répartition des zéros des fonctions $L$ et matrices aléatoires.)

À la recherche de petites sommes d'exponentielles. (In search of small exponential sums).

On the dimension of the space of cusp forms associated to 2-dimensional complex Galois representations

Rankin-Selberg $L$-functions in the level aspect

Zeros of families of automorphic $L$-functions close to 1

Simultaneous nonvanishing of twists of automorphic $L$-functions

The second moment of the symmetric square $L$-functions

Two non-vanishing theorems of special values of $L$-functions. (Deux théorèmes de non-annulation de valeurs spéciales de fonctions $L$.)

Appendice de "Sur la nature non-cyclotomique des points d'ordre fini des courbes elliptiques" par L. Merel

Exponential decay in the frequency of analytic ranks of automorphic $L$-functions

Mollification of the fourth moment of automorphic $L$-functions and arithmetic applications

Simultaneous approximation of real numbers by rational numbers and its application to the Boltzmann equation. (Approximation simultanée de réels par des nombres rationnels et noyau de collision de l'équation de Boltzmann.)

Explicit upper bound for the (analytic) rank of $J_0(q)$

Non-vanishing of high derivatives of Dirichlet $L$-functions at the central point

A lower bound for the rank of $J_0(q)$

Non-vanishing of high derivatives of automorphic $L$-functions at the center of the critical strip

The analytic rank of $Jsub 0(q)$ and zeros of automorphic $L$-functions

On the zeros of $L$-functions on function fields. (Sur les zéros de fonctions $L$ sur les corps de fonctions.)

On some exponential sums over primes. (Sur certaines sommes d'exponentielles sur les nombres premiers.)

Recent progress of the sieve and applications [after Duke, Fouvry, Friedlander, Iwaniec]. (Progrès récents du crible et applications [d'après Duke, Fouvry, Friedlander, Iwaniec].)

Lower bounds of exponential sums. (Minorations de sommes d'exponentielles.)

On the Sato-Tate conjecture for Kloosterman sums. II. (Autour de la conjecture de Sato-Tate pour les sommes de Kloosterman. II.)

Points of small height on the modular curves $X_0(N) $. (Points de petite hauteur sur les courbes modulaires $X_0(N)$.)

The rank of families of abelian varieties. (Le rang de familles de variétés abéliennes.)

Average rank of families of elliptic curves and Sato-Tate laws. (Rang moyen de familles de courbes elliptiques et lois de Sato-Tate.)

On the Sato-Tate conjecture for Kloosterman sums. (Autour de la conjecture de Sato-Tate pour les sommes de Kloosterman. I.)

Teaching & PhD

PhD Students

Past EPFL PhD Students

Courses

Advanced analytic number theory

Advanced linear algebra I - vector spaces