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Second moment of the GL_3 standard L-function on the critical line. (Online)
Mathew P. YoungICTS:30201 -
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Radio Cosmology and Continuum Observations in the SKA Era: A Synergic View
The Square Kilometre Array (SKA), set to begin operations in 2027, will be the world’s largest radio telescope marking one of the great scientific and engineering feats of the 21st century. The SKA will advance a wide range of research areas within astronomy, with a major focus on cosmology and radio continuum science at low and mid frequencies. Despite their different objectives, these two fields share a substantial overlap and thus stand to benefit from collaborative efforts in joint observation strategies, data calibration, and innovative analysis techniques.This two week long program aims to bring together national and international experts in radio cosmology and continuum science, fostering collaboration and training the next generation of researchers in these areas. The program will have two main components: a program and a school.The program (7-11 April 2025) will focus on the current state of observation, modelling, and inference tools for radio cosmology and continuum science....
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Beyond the Horizon: Testing the black hole paradigm
We are living in an exciting era of great discoveries in the field of gravitational physics. The detection of gravitational waves by the LIGO-VIRGO-KAGRA (LVK) collaboration starting from 2016 has already led to an enormous interest in various aspects of the physics of compact objects. The recent observations of the shadows of the galactic centers for M87 and Milky Way, by the Event Horizon Telescope (EHT), have further resulted into diverse research programs on the nature of compact objects. The primary emphasis of these observations is to test the theory of general relativity at the strong-field regime and to understand the nature of the astrophysical compact objects. Several recent developments led to the extensive use of various new mathematical and computational techniques to probe the physics associated with these compact objects. The primary motivation of the school would be to learn from leading researchers about several crucial aspects of the physics of compact objects. The p...
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Decisions, Games, and Evolution
Cooperation is seen across all biological scales ranging from cells to societies. In organisms like bacteria, the decision-making process is genetically hardwired but higher animals endowed with cognitive abilities have to make choices that can affect not only their own survival but also that of their group.Uncovering the organizing principles that lead to evolution of cooperation is an issue of fundamental importance that transcends disciplinary boundaries. Insights can be obtained from studying biological communities, through mathematical and agent-based modeling, cognitive science, social network dynamics and behavioral economics. Such investigations can also lead to the understanding of other intriguing evolutionary phenomena like opinion dynamics, evolution of fairness and spiteful behaviour. Evolutionary Game Theory provides a powerful framework for addressing such questions in the context of both biological and cultural evolution. In this program, we will therefore be addressin...
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New trends in Teichmüller theory
This is a two-week thematic program with a focus on recent developments in Teichmüller theory which promise to be fertile in the near future. These includeThe metric theory of Teichmüller spaces and other spaces, including the recent breakthroughs in the Thurston metric.Higher Teichmüller theory, and its interplay with Higgs bundles, algebraic geometry and Anosov representations.The Teichmüller theory of infinite-type surfaces, including their quasiconformal theory and what is known as the ``big" mapping class group.Relations with anti-de Sitter geometry.The techniques for these areas come from complex analysis, hyperbolic geometry, dynamics, partial differential equations, projective geometry, geometric and combinatorial group theory, algebraic geometry, Kähler geometry and other fields — these often give several points of view on the same objects showing the richness of the theory.The workshop will consist of a series of mini-courses (with lectures typically totalling 3 hours) toget...
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Positive Geometry in Scattering Amplitudes and Cosmological Correlators
The workshop aims to bring together experts from two different disciplines: mathematical aspects of scattering amplitudes, and cosmology. In the last decades we have got a tremendous amount of insights in the structure of perturbative on-shell scattering amplitudes. This includes unitarity methods, recursion relations, worldsheet models, bootstrap methods and more recently also an intriguing connection to positive geometry, positive Grassmannian, Associahedron and the Amplituhedron. This all pushes us closer to a reformulation of the perturbative S-matrix using a completely new set of principles. At the same time, similar remarkable structures have been observed in cosmological correlators, which are fundamental objects capturing the physics of our Universe. This connects two seemingly different fields of theoretical physics. This workshop will help to advance these connections further.Eligibility criteria:Registrations for the PGSAC Program are open to graduate students and researcher...
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Quantum Trajectories
The progress in parallel of high-speed electronics and low temperature technologies has revolutionized the study of quantum matter. Many of the gedanken experiments of the fathers of quantum mechanics are now realized routinely, as well as many new ones that the founders could hardly have dreamed of. The possibility of quantum-based encryption, communication and computing is getting concrete and some real implementations are already available. This so-called second quantum revolution which is mostly yet to come will be the fruit of a close collaboration between theory (theoretical physics, but also applied mathematics) and experiment.Our aim is to address some of the central theoretical open questions in the field. The program will be centered around three main topics:(i) Quantum trajectories and Quantum control,(ii) Measurement induced phase transitions and finally,(iii) Quantum information and computation.The goal of this program is to gather researchers from the above areas, from t...
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ICTP-ICTS Winter School on Quantitative Systems Biology
Ecosystems embody a remarkable diversity of life, forming intricate networks that exhibit both stability and the potential for rapid change. These systems, governed by complex interactions among organisms and their environment, present a rich tapestry for scientific exploration. This Winter School on Quantitative Systems Biology (QSB) will dive into the heart of understanding how biodiversity underpins ecosystem stability, resilience, and the mechanisms that drive their dynamics. We will explore cutting-edge questions such as: How does biodiversity contribute to the robustness of ecosystems against perturbations? What are the underlying principles that predict the stability of ecosystems? What happens to ecosystem dynamics when they become unstable? And how can we model the interplay between species to understand potential critical or tipping points? Through a multidisciplinary approach that combines theory with data, participants will engage with the latest methodologies and tools in ...
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Hearing beyond the standard model with cosmic sources of Gravitational Waves
The experimental detection of gravitational waves (GWs) due to the merger of astrophysical objects like black holes and neutron stars is one of the biggest discoveries in physics. The GWs can also be sourced from several other cosmological phenomena, and their amplitudes and frequencies vary in a wide range. The detection of these gravitational waves can potentially probe fundamental physics beyond the Standard Model (BSM) of particle physics and cosmology. For example, inflation is associated with several sources of tensor perturbations during inflation and the ones generated during reheating and preheating. Each of these propagates as detectable Stochastic GW background (SGWB) signals. Associated with inflation is also the collapse of density fluctuations to form Primordial Black Holes (PBH), leaving signatures in induced GWs and non-gaussianities. Cosmological first-order Phase Transitions (PT) during which the universe transitions from a false vacuum to a true vacuum leads to bubbl...
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Indo-French workshop on Classical and quantum dynamics in out of equilibrium systems
Organized with support from CEFIPRA The idea of this Indo-French workshop is to gather specialists in the field of classical and quantum out-of-equilibrium dynamics and to initiate collaborative research programs, training programs and scientific exchanges between the two countries.Recently a joint Indo-French international research project (IRP) on "Classical and quantum dynamics in out of equilibrium systems" was proposed between several laboratories of theoretical physics in France and in India. CNRS has approved this project whose Principal Investigators are Satya Majumdar (LPTMS), Gregory Schehr (LPTHE), Gautam Mandal (TIFR) and Manas Kulkarni (ICTS). The goal of the CEFIPRA supported workshop is to bring together people within this Indo-French international research project (and people not involved directly in the project) so that they can identify areas of common interests leading to possible future collaborations.There is much interest on the French side, in CNRS as well ...
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Combinatorial Methods in Enumerative Algebra
Many algebraic counting problems give rise to integer sequences that hold information which is best accessed by encoding these numbers in appropriate generating functions. Numerous classical zeta and L-functions testify to this principle: Dirichlet’s zeta function enumerates ideals of a number field; Witten’s zeta function counts representations of Lie groups; Hasse– Weil zeta functions encode the numbers of rational points of algebraic varieties over finite fields. Analytic and arithmetic properties of these zeta functions hold or are expected to hold, the key to a treasure trove of information about the underlying structures.Zeta functions of groups and rings are invaluable tools in asymptotic group theory and ring theory. Often, they admit Euler product decompositions, with rational local factors that reflect regularity of structure in the underlying data.We aim to bring together experts in the various relevant subject areas, including those in zeta functions of groups and rings and...
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Moist convective dynamics of Monsoons
Cloud clusters cover a wide range of scales: from the turbulent cloud cluster that we observe in the sky with our naked eyes to the gigantic organized cloud bands such as Monsoons, The Inter-Tropical Convergence Zone (ITCZ), Cyclones, the Madden-Julian oscillation (MJO) etc. that satellites observe. On these different scales clouds either aggregate through their own local cloud-circulation feedbacks or sometimes they are seen to ride on top of vortices linked to waves and instabilities. Although the monsoon dynamics has been studied for a long time, how monsoon convection organizes on a variety of time-scales is an unresolved enigma. This program will be organized around this unresolved scientific direction.Topics covered will include:Geophysical fluid dynamics of moist flows: Intro to GFD, Shallow Water equations, Two-layer models, Moist dynamics on equatorial beta plane, Waves and Instabilities, Idealised modeling, parameterisation of precipitation in GFD models.Physics of convectiv...
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Circle Method and Related Topics
Even after one hundred years, the circle method remains one of the most important tools in the analytic theory of numbers. Over the years the method has gone through several modifications, resulting in novel applications. Originally introduced to study the partition function and the Waring problem, the circle method quickly became the most powerful analytic tool to count rational points on varieties. It was also adopted to study problems in the prime number theory. Recently the circle method has been extended to function fields and general number fields, and has been put on a broader adelic and geometric setting. We have also seen some striking recent applications in areas such as analytic theory of L-functions, ergodic theory, and the Langlands program. This workshop will present accessible short lecture series on the circle method and related topics, from experts in the field, aimed at senior graduate students and post-docs. The main aim will be to introduce the audience to various f...