Generating Functions Some Examples by J-M Deshouillers @ICTStalks

Generating Functions Some Examples by J-M Deshouillers @ICTStalks

Uploaded June 2026 | Updated September 2026, 2 weeks ago

Discussion Meeting

The Classical Circle Method and the Large Sieve

ORGANIZERS: R. Balasubramanian (IMSc, Chennai, India), Prahlad Sharma (IIT Kanpur, India) and Saurabh Kumar Singh (IIT Kanpur, India)

DATE & TIME: 04 May 2026 to 08 May 2026

VENUE: Ramanujan Lecture Hall, ICTS Bengaluru

The circle method originated in the pioneering work of G. H. Hardy and S. Ramanujan on the partition function and was later refined by Hardy and Littlewood in their study of Waring’s problem. Since then, it has become a central tool in analytic number theory, leading to many striking applications, including the ternary Goldbach conjecture, which states that every odd integer greater than 5 can be written as the sum of three prime numbers.

This workshop aims to develop an understanding of the ideas and techniques underlying proofs obtained via the circle method. We will explore the analytic techniques and key ideas behind these proofs, with an emphasis on both classical and modern developments. A central theme of the workshop will be the close relationship between the circle method and the large sieve, and how large sieve techniques can be used to enhance the effectiveness of the circle method. Participants will have ample opportunities for interaction, including discussions with leading experts, the presentation of open problems, and collaborative exploration of new directions.

Eligibility criteria: The program is open to PhD students, postdoctoral researchers, and faculty with a background in number theory. Exceptionally motivated Master’s students with strong preparation in analytic number theory may also apply.

Accommodation will be provided for outstation participants at our on campus guest house.

ICTS is committed to building an environment that is inclusive, non-discriminatory and welcoming of diverse individuals. We especially encourage the participation of women and other under-represented groups.

CONTACT US: ccmls@icts.resi.n
PROGRAM LINK: icts.res.in/discussion-meeting/ccmls2026

Generating Functions Some Examples by J-M Deshouillers

Project 2: Lecture 3 by Adrian Roellin

$Transience and Non-ergodicity in a Model of Many Sokobans and Boxes on a Line by Priyadharshini V Discussion Meeting: 11th Indian Statistical Physics Community Meeting ORGANIZERS: Ranjini Bandyopadhyay (RRI India), Abhishek Dhar (ICTS-TIFR, India), Kavita Jain (JNCASR, India), Rahul Pandit (IISc, India), Sanjib Sabhapandit (RRI India) and Samriddhi Sankar Ray (ICTS-TIFR, India) DATE & TIME: 27 April 2026 to 29 April 2026 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru This is an annual discussion meeting of the Indian statistical physics community attended by scientists, postdoctoral fellows and graduate students, from across the country, working in the broad area of statistical physics. This meeting will be the 11th in the series. The following list of topics, that are covered in STATPHYS meetings of the International Union of Pure and Applied Physics, will be covered in this discussion meeting. General and mathematical aspects Rigorous results, exact solutions, probability theory, stochastic field theory, phase transitions and critical phenomena at equilibrium, information theory, optimization, etc. Out-of-equilibrium aspects Driven systems, transport theory, relaxation and response dynamics, random processes, anomalous diffusion, fluctuation theorems, large deviations, out-of-equilibrium phase transitions, etc. Quantum fluids and condensed matter Strongly correlated electrons, cold atoms, graphene, mesoscopic quantum phenomena, fractional quantum Hall effect, low dimensional quantum field theory, quantum phase transitions, quantum information, entanglement, Lüttinger liquid, spin liquid, etc. Disordered and glassy systems Percolation, spin glasses, structural glasses, metallic glasses, jamming, glass transition, algorithmic problems, etc. Biological physics Molecular motors, single and multicellular dynamics, bacteria, swimmers, spatio-temporal organization, biological membranes, biopolymer folding, genomics, biological networks, evolution models, evolutionary game theory, etc. Soft matter Simple and complex fluids, active matter, molecular and ionic fluids,wetting, self-assembly, polymers, gels, liquid crystals, microemulsions, foams, membranes, colloids, granular materials, etc. Nonlinear physics Dynamical systems, chaos (classical and quantum), pattern formation, chemical reactions, hydrodynamic instabilities, turbulence (classical and quantum), etc. Interdisciplinary and complex systems Networks and graphs, epidemics, econophysics, social phenomena, traffic flow, ecology, etc. CONTACT US: ispcm@icts.res.in PROGRAM LINK: https://icts.res.in/discussion-meeting/ispcm2026$

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$Information Phases of Projected Ensembles in Scrambling Dynamics by Allan Sherry Discussion Meeting: 11th Indian Statistical Physics Community Meeting ORGANIZERS: Ranjini Bandyopadhyay (RRI India), Abhishek Dhar (ICTS-TIFR, India), Kavita Jain (JNCASR, India), Rahul Pandit (IISc, India), Sanjib Sabhapandit (RRI India) and Samriddhi Sankar Ray (ICTS-TIFR, India) DATE & TIME: 27 April 2026 to 29 April 2026 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru This is an annual discussion meeting of the Indian statistical physics community attended by scientists, postdoctoral fellows and graduate students, from across the country, working in the broad area of statistical physics. This meeting will be the 11th in the series. The following list of topics, that are covered in STATPHYS meetings of the International Union of Pure and Applied Physics, will be covered in this discussion meeting. General and mathematical aspects Rigorous results, exact solutions, probability theory, stochastic field theory, phase transitions and critical phenomena at equilibrium, information theory, optimization, etc. Out-of-equilibrium aspects Driven systems, transport theory, relaxation and response dynamics, random processes, anomalous diffusion, fluctuation theorems, large deviations, out-of-equilibrium phase transitions, etc. Quantum fluids and condensed matter Strongly correlated electrons, cold atoms, graphene, mesoscopic quantum phenomena, fractional quantum Hall effect, low dimensional quantum field theory, quantum phase transitions, quantum information, entanglement, Lüttinger liquid, spin liquid, etc. Disordered and glassy systems Percolation, spin glasses, structural glasses, metallic glasses, jamming, glass transition, algorithmic problems, etc. Biological physics Molecular motors, single and multicellular dynamics, bacteria, swimmers, spatio-temporal organization, biological membranes, biopolymer folding, genomics, biological networks, evolution models, evolutionary game theory, etc. Soft matter Simple and complex fluids, active matter, molecular and ionic fluids,wetting, self-assembly, polymers, gels, liquid crystals, microemulsions, foams, membranes, colloids, granular materials, etc. Nonlinear physics Dynamical systems, chaos (classical and quantum), pattern formation, chemical reactions, hydrodynamic instabilities, turbulence (classical and quantum), etc. Interdisciplinary and complex systems Networks and graphs, epidemics, econophysics, social phenomena, traffic flow, ecology, etc. CONTACT US ispcm@icts.res.in PROGRAM LINK https://icts.res.in/discussion-meeting/ispcm2026$ $Graphene Quantum Hall by Sumathi Rao Discussion Meeting: 11th Indian Statistical Physics Community Meeting ORGANIZERS: Ranjini Bandyopadhyay (RRI India), Abhishek Dhar (ICTS-TIFR, India), Kavita Jain (JNCASR, India), Rahul Pandit (IISc, India), Sanjib Sabhapandit (RRI India) and Samriddhi Sankar Ray (ICTS-TIFR, India) DATE & TIME: 27 April 2026 to 29 April 2026 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru This is an annual discussion meeting of the Indian statistical physics community attended by scientists, postdoctoral fellows and graduate students, from across the country, working in the broad area of statistical physics. This meeting will be the 11th in the series. The following list of topics, that are covered in STATPHYS meetings of the International Union of Pure and Applied Physics, will be covered in this discussion meeting. General and mathematical aspects Rigorous results, exact solutions, probability theory, stochastic field theory, phase transitions and critical phenomena at equilibrium, information theory, optimization, etc. Out-of-equilibrium aspects Driven systems, transport theory, relaxation and response dynamics, random processes, anomalous diffusion, fluctuation theorems, large deviations, out-of-equilibrium phase transitions, etc. Quantum fluids and condensed matter Strongly correlated electrons, cold atoms, graphene, mesoscopic quantum phenomena, fractional quantum Hall effect, low dimensional quantum field theory, quantum phase transitions, quantum information, entanglement, Lüttinger liquid, spin liquid, etc. Disordered and glassy systems Percolation, spin glasses, structural glasses, metallic glasses, jamming, glass transition, algorithmic problems, etc. Biological physics Molecular motors, single and multicellular dynamics, bacteria, swimmers, spatio-temporal organization, biological membranes, biopolymer folding, genomics, biological networks, evolution models, evolutionary game theory, etc. Soft matter Simple and complex fluids, active matter, molecular and ionic fluids,wetting, self-assembly, polymers, gels, liquid crystals, microemulsions, foams, membranes, colloids, granular materials, etc. Nonlinear physics Dynamical systems, chaos (classical and quantum), pattern formation, chemical reactions, hydrodynamic instabilities, turbulence (classical and quantum), etc. Interdisciplinary and complex systems Networks and graphs, epidemics, econophysics, social phenomena, traffic flow, ecology, etc. CONTACT US ispcm@icts.res.in PROGRAM LINK https://icts.res.in/discussion-meeting/ispcm2026$ $Rotational Dynamics of Passive Clusters in Chiral Active Baths by Divya Kushwaha Discussion Meeting: 11th Indian Statistical Physics Community Meeting ORGANIZERS: Ranjini Bandyopadhyay (RRI India), Abhishek Dhar (ICTS-TIFR, India), Kavita Jain (JNCASR, India), Rahul Pandit (IISc, India), Sanjib Sabhapandit (RRI India) and Samriddhi Sankar Ray (ICTS-TIFR, India) DATE & TIME: 27 April 2026 to 29 April 2026 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru This is an annual discussion meeting of the Indian statistical physics community attended by scientists, postdoctoral fellows and graduate students, from across the country, working in the broad area of statistical physics. This meeting will be the 11th in the series. The following list of topics, that are covered in STATPHYS meetings of the International Union of Pure and Applied Physics, will be covered in this discussion meeting. General and mathematical aspects Rigorous results, exact solutions, probability theory, stochastic field theory, phase transitions and critical phenomena at equilibrium, information theory, optimization, etc. Out-of-equilibrium aspects Driven systems, transport theory, relaxation and response dynamics, random processes, anomalous diffusion, fluctuation theorems, large deviations, out-of-equilibrium phase transitions, etc. Quantum fluids and condensed matter Strongly correlated electrons, cold atoms, graphene, mesoscopic quantum phenomena, fractional quantum Hall effect, low dimensional quantum field theory, quantum phase transitions, quantum information, entanglement, Lüttinger liquid, spin liquid, etc. Disordered and glassy systems Percolation, spin glasses, structural glasses, metallic glasses, jamming, glass transition, algorithmic problems, etc. Biological physics Molecular motors, single and multicellular dynamics, bacteria, swimmers, spatio-temporal organization, biological membranes, biopolymer folding, genomics, biological networks, evolution models, evolutionary game theory, etc. Soft matter Simple and complex fluids, active matter, molecular and ionic fluids,wetting, self-assembly, polymers, gels, liquid crystals, microemulsions, foams, membranes, colloids, granular materials, etc. Nonlinear physics Dynamical systems, chaos (classical and quantum), pattern formation, chemical reactions, hydrodynamic instabilities, turbulence (classical and quantum), etc. Interdisciplinary and complex systems Networks and graphs, epidemics, econophysics, social phenomena, traffic flow, ecology, etc. CONTACT US: ispcm@icts.res.in PROGRAM LINK: https://icts.res.in/discussion-meeting/ispcm2026$ $Query Complexity - Quantifying What You Need to Know by Meena Mahajan Program: Summer School for Women in Mathematics and Statistics ORGANIZERS: Nikita Agarwal (Delhi University, India), Siva Athreya (ICTS-TIFR Bengaluru, India), Rhythm Grover (IIT Guwahati, India), Kannappan Sampath (IISER Pune, India) and Dootika Vats (IIT Kanpur, India) DATE & TIME: 08 June 2026 to 19 June 2026 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru The summer school is intended for women students studying in first year B.A/B.Sc./B.E./B.Tech. or equivalent degree and having Mathematics as one of the major subjects/courses, during the academic year 2025-2026. Over a period of two weeks, the school aims to help the students gain broader exposure to problem solving skills in mathematics and statistics at the undergraduate level. Specific topics that will be covered are: •⁠ ⁠Calculus: - Curve Sketching - Sequences, Limits, and limit points - Negation and logical deduction •⁠ ⁠Functions: - Iterative functions - Contractions, fixed points •⁠ ⁠Construction of fractals via contraction maps •⁠ ⁠⁠Linear Algebra - Column space, row space, eigenspace •⁠ ⁠Conditional Probability and Markov chains •⁠ ⁠⁠R-programming - Simulating fractals - Simulating Markov chains There will be problem solving sessions across topics. Each topic will have a brief introductory lecture session on a focus area followed by problem-solving sessions on it. The participants are expected to work together to solve the problem sheets that will be given out in these sessions. Each day will also feature popular science lectures by distinguished researchers and professionals. The topics will be diverse, not limited to mathematics and statistics, and the lectures will be made accessible to all the participants. Other daily events will include post dinner problem solving sessions and discussions with popular science speakers of the day. Further, there will be many opportunities to interact with women scientists who will visit the program for short periods. CONTACT US: swms@icts.res.in PROGRAM LINK: https://icts.res.in/program/swms2026$

First Passage Problems: Classical and Quantum (Lecture 4) by Abhishek Dhar

International Centre for Theoretical Sciences |

Generating Functions Some Examples by J-M Deshouillers