4 MAR 2025
11:00 - 12:30

Abstract:



We explore a scenario in which dark matter is a massive bosonic field, arising solely from quantum fluctuations generated during inflation. In this framework, dark matter exhibits primordial isocurvature perturbations with an amplitude of O(1) at small scales that are beyond the reach of current observations, such as those from the CMB and large-scale structure. Assuming a monochromatic initial power spectrum, we identify the viable parameter space defined by dark matter mass and the length scale of perturbations. A key prediction of this scenario is copious formation of subsolar dark matter halos at high redshifts. Observational confirmation of a large population of such low-mass halos will support the hypothesis that dark matter originated purely from inflationary quantum fluctuations.

[Based on arXiv:2501.03444]

5 MAR 2025
17:30 - 19:00

Seen through the lens of the Minimal Model Program, the classification of algebraic varieties can be summarised into two main steps: firstly, the algorithm of the MMP allows to decompose a variety with mild singularities, birationally, into a tower of fibrations whose general fibres have ample, anti-ample, or numerically trivial canonical divisor. In view of this decomposition, the natural second step to take is to study these 3 classes of algebraic varieties in detail, for example, studying their moduli theory and/or any other property that could shed light on ways to understand all possible elements that belong to such classes. It turns out a very important property to understand in this process is boundedness: a collection of varieties is bounded when the elements of the given collection can be parametrised using a finite type geometric space. The property of boundedness plays a crucial role in the construction of proper moduli spaces of finite type. Moreover, if a given collection of algebraic varieties is bounded (in char 0), then the topological types of their underlying analytic spaces belong to only finitely many homeomorphism classes: hence, all of their topological invariants come in just finitely many possible different versions. While over the past 15 years, several breakthroughs have completely settled the question of boundedness (and the subsequent construction of moduli spaces) in the case of log canonical models (varieties/pairs with ample canonical divisor) and Fano varieties (those with anti-ample canonical divisor), the situation is still quite unclear in the case of trivial numerical divisor. In this seminar, I will try to explain what is known, or not, and what those challenges are that make the situation quite more complicated than the other 2 cases. I will moreover explain how we can overcome most of the issues if we assume that a K-trivial variety is endowed with a fibration structure of relative dimenesion one. The seminar includes results from various works I developed over the past 10 years with G. Di Cerbo, C. Birkar, S. Filipazzi, and C. Hacon. Moreover, I will talk about current work in progress with P. Engel, S. Filipazzi, F. Greer, M. Mauri were we show various new boundedness results for K-trvial varieties fibered in K3 surfaces or abelian varieties.

https://zoom.us/join
Meeting ID: 9086116889
Passcode: 362880
Website: http://math.ipm.ac.ir/agnt/
Venue: , (Zoom Lecture)

6 MAR 2025
14:00 - 16:00

Mathematicians have used machines and datasets to aid their research for millennia. In our time, computational tools such as computer algebra systems, SAT/SMT solvers, Reinforcement Learning, and LLMs play an increasingly central role in mathematical discovery. Complementing these, formal verification and proof assistants ensure the correctness of mathematical arguments, providing mathematicians with instant and extremely high confidence in formalized results and enabling large-scale collaboration. This formal proof revolution is transforming how we produce, organize, and interact with mathematical knowledge.
In this talk, I will introduce Lean, a popular proof assistant based on dependent type theory. I will give an overview of Lean's community-based mathematical library Mathlib. I will survey the state of the art in using Lean in mathematical research. Finally, I will highlight Lean's powerful metaprogramming framework, and how we are employing it in a new collaborative project to bring Homotopy Type Theory (HoTT) and synthetic homotopical reasoning into Lean4.

Zoom room information:
https://us06web.zoom.us/j/81916335336?pwd=5zQT4lutMiBoY5Xp1pkFGtbqiaGozg.1
Meeting ID: 819 1633 5336
Passcode: 559618
Venue: Niavaran, Lecture Hall 1

8 APR 2025
09:00 - 16:00

Perceptual decision making: A neurobiological introduction - Workshop


Link: https://scs.ipm.ac.ir/new/docs/psycho1403.pdf

17 APR 2025
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۲۹-۲۸ فروردین ۱۴۰۴ (۱۷-۱۸ آوریل ۲۰۲۵)

Link: https://physics.ipm.ac.ir/conferences/ishep2025/index.jsp

18 APR 2025
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۲۹-۲۸ فروردین ۱۴۰۴ (۱۷-۱۸ آوریل ۲۰۲۵)

Link: https://physics.ipm.ac.ir/conferences/ishep2025/index.jsp