18 SEP 2024
16:00 - 17:00

We present further families of Abelian varieties which contradict Zarhin's conjecture about mictoweights in positive characteristic.
Venue: Niavaran, Lecture Hall 1

11 SEP 2024
14:00 - 16:00

This talk focuses on pointwise ergodic theorems and their connection to Bourgain's path to his Fields Medal. We aim to cover four key milestones:
Part One: We investigate the norm convergence of ergodic averages, concluding with an explanation of the Baby Spectral Theorem.
Part Two: We examine the pointwise ergodic theorem established by Birkhoff in 1931. Depending on the time available, we will cover at least one proof, exploring Calderon's transference in the process.
Part Three: This section delves into the circle method and its comparison to the continuous Fourier Transform. We will also discuss several properties of prime numbers and provide an approximation for averages along primes.
Part Four: We introduce the concept of oscillation and present a proof of the pointwise ergodic theorem along primes. Time permitting, we will explore further developments post-1990.

The references are uploaded in the following link:
https://drive.google.com/drive/folders/1_zIDuDybfkfYuHhrlLtwe-rd6SdpraPZ?usp=drive_link
Venue: Niavaran, Lecture Hall 1

11 SEP 2024
10:00 - 12:00

This talk focuses on pointwise ergodic theorems and their connection to Bourgain's path to his Fields Medal. We aim to cover four key milestones:
Part One: We investigate the norm convergence of ergodic averages, concluding with an explanation of the Baby Spectral Theorem.
Part Two: We examine the pointwise ergodic theorem established by Birkhoff in 1931. Depending on the time available, we will cover at least one proof, exploring Calderon's transference in the process.
Part Three: This section delves into the circle method and its comparison to the continuous Fourier Transform. We will also discuss several properties of prime numbers and provide an approximation for averages along primes.
Part Four: We introduce the concept of oscillation and present a proof of the pointwise ergodic theorem along primes. Time permitting, we will explore further developments post-1990.

The references are uploaded in the following link:
https://drive.google.com/drive/folders/1_zIDuDybfkfYuHhrlLtwe-rd6SdpraPZ?usp=drive_link
Venue: Niavaran, Lecture Hall 1

11 SEP 2024
18:00 - 19:30

In this talk, I explore the evolution of types or species in populations from both genetic and genomic perspectives. I first discuss the Fleming-Viot (FV) process in random environment, a measure-valued diffusion modeling the evolution of type-frequencies in countable populations subject to genetic drift, mutation, and selection. The random environment introduces fluctuating fitness among types, meaning their relative strength compared to each other varies stochastically over time. This makes the model significantly more complex than the classical version. I then briefly describe a more general model where multiple FV processes coexist, with interacting and fluctuating fitnesses, allowing competition and collaboration between types and populations. Key results include ergodic behavior and averaging theorems, which are established using dual representations that involve intricate function-valued Markov processes. In the second part, I model genome evolution as continuous-time random walks on groups and graphs, establishing a framework for phylogeny reconstruction of genomes sampled at random from the evolutionary process. A geometric median of a set A in a metric space (S,d) is a point x whose sum of distances to points of A, i.e. ∑_(y∈S)▒d(x,y) , is minimized. I highlight the role of geometric medians in estimating the true ancestor of sampled genomes and present conditions under which medians provide accurate estimations. Finally, I conclude by emphasizing key applications of these models in evolutionary biology and population genetics.

https://us06web.zoom.us/j/86042917248?pwd=YOAG1B0ePOSpipAnqPwM8PDPyiM1ti.1
Meeting ID: 860 4291 7248
Pass Code: 362880
Venue: , (Online)

11 SEP 2024
16:00 - 17:30

In this talk, I will present probabilistic and statistical models addressing problems in population genetics and genome rearrangements. Population models can be classified into two types: those with a constant population size, like the Moran process, and those with a stochastically varying population size, as in branching processes. I will begin by focusing on the structured Moran process, where populations reside on geometric structures (vertices of graphs). These models capture the effects of population geometry on evolutionary dynamics by incorporating frequency-dependent fitness and spatial constraints. I will demonstrate methods for approximating fixation probabilities on star-shaped graphs and other geometric structures using solutions to differential equations, with applications to cancer evolution. I will briefly discuss recent work on modeling the accumulation of genetic variants using branching processes. Finally, I will explore combinatorial problems in genome rearrangements, focusing on the breakpoint median problem, which is central to phylogeny reconstruction. I will explain how to construct approximate medians of random genomes. I will also introduce an algorithm for finding all breakpoint medians and address the challenges in constructing intermediate genomes.
https://us06web.zoom.us/j/86042917248?pwd=YOAG1B0ePOSpipAnqPwM8PDPyiM1ti.1
Meeting ID: 860 4291 7248 Passcode: 362880
Venue: , (Online Seminar)

14 AUG 2024
10:00 - 12:00

One of the first steps in studying three-dimensional manifolds is the Poincaré conjecture. This conjecture states that every simply connected, closed, and orientable three-dimensional manifold is homeomorphic to the 3-sphere. In the 1980s, Thurston formulated a stronger conjecture than the Poincaré conjecture. Thurston's Geometrization Conjecture states that every closed, orientable, and prime three-dimensional manifold can be cut along a number of tori such that the interior of each resulting manifold has one of Thurston's eight geometric structures with finite volume. In dimension 2, the Geometrization Conjecture reduces to the uniformization theorem. Our goal is to study the decomposition theorems for three-dimensional manifolds (the Prime Decomposition and JSJ Decomposition) and then examine Thurston's eight geometries to precisely state the Geometrization Conjecture. Following this, we will explore some consequences of this conjecture, such as the fact that the fundamental group is almost a complete invariant for closed three-dimensional manifolds.

Some references:
Three-Dimensional Geometry and Topology, William P. Thurston and Silvio Levy
An Introduction to Geometric Topology, Bruni Martelli
Venue: Niavaran, Lecture Hall 1

14 AUG 2024
14:00 - 16:00

One of the first steps in studying three-dimensional manifolds is the Poincaré conjecture. This conjecture states that every simply connected, closed, and orientable three-dimensional manifold is homeomorphic to the 3-sphere. In the 1980s, Thurston formulated a stronger conjecture than the Poincaré conjecture. Thurston's Geometrization Conjecture states that every closed, orientable, and prime three-dimensional manifold can be cut along a number of tori such that the interior of each resulting manifold has one of Thurston's eight geometric structures with finite volume. In dimension 2, the Geometrization Conjecture reduces to the uniformization theorem. Our goal is to study the decomposition theorems for three-dimensional manifolds (the Prime Decomposition and JSJ Decomposition) and then examine Thurston's eight geometries to precisely state the Geometrization Conjecture. Following this, we will explore some consequences of this conjecture, such as the fact that the fundamental group is almost a complete invariant for closed three-dimensional manifolds.

Some references:
Three-Dimensional Geometry and Topology, William P. Thurston and Silvio Levy
An Introduction to Geometric Topology, Bruni Martelli
Venue: Niavaran, Lecture Hall 1

10 JUL 2024
14:00 - 16:00

There are different types of approaches to solve P vs NP, some of them are logical approaches. The lecturer's PhD thesis [11] is based on one of these logical approaches 2002 [2], [6]. Till 2011, he and some other logicians made an unsuccessful aƩempt to shed light on this problem in this way. In 2010‐2011, he started to introduce another logical approach based on paradoxes, more specifically ?Unexpected Hanging Paradox?. The goal is to use paradoxes similar to applying paradoxes (Liar Paradoxes) in the Godel?s Incompleteness Theorem [14], [15], [16]. In [5], [16] (2017), he showed by defining a new version of this paradox, we face a contradiction, not a paradox. To cope with this situation, in 2019 Fuzzy Time [4], [17] (or as some of the speaker?s colleagues used it later on, Temporal Continuum (2023) or Continuity in Time (2024)) came into the centre of the subject and discussion. Nevertheless, we have concepts similar to the fuzziness of Time and space in the history of science, Mathematics, Philosophy and Physics [7], [12], [13]. Based on that, the speaker claimed a new interpretation of Quantum Mechanics, the ?Fuzzy time‐particle? interpretation of Quantum Mechanics [1], [3], [4]. ?Theory of Fuzzy Time Computation?, is introduced in [8], [9], [10], monthly seminars of the Iranian Association of Logic [18], and The 10th annual conference of the Iranian Association for Logic (IAL) (2023) [19]. In 2023, this Theory was introduced in a paper in HAL [9] and now it is in development. In this lecture, after defining this Theory, we explain a part of it in details, and as the main conclusion, we prove TC+CON(TC^* )ͰP≠NP.
Join Zoom Meeting
https://us06web.zoom.us/j/9086116889?pwd=WGRFOGZWZ1FOMXJrcWpJMWFqUFIvQT09&omn=88907944379
Meeting ID: 908 611 6889
Passcode: 362880
Venue: Niavaran, Lecture Hall 2





References.
1. Computing Fuzzy Time Function, F.Didehvar, Philpapers, SSRN 2022
2. B.Poizat, Les petit cailloux. Une approach modele-theorique de l?Algorithmie , Nur al-Mantiq wal-Ma?rifah, no.3.Ale?as, Lyon 1995, 2 pp.
3. Does accepting Fuzzy Time-Particle interpretation of Quantum Mechanics, refutes the other interpretations? (Is fuzziness of time checkable experimentally?), F.Didehvar, Philpapers, SSRN, 2021
4.Fuzzy time a solution for unexpected hanging Paradox ( a Fuzzy interpretation Of Quntum Mechanics)), Philpapers 2019-4-13
5. Is Classical Mathematics appropriate for Theory of Computation? F.Didehvar, Philpapers(Manuscript), 2017,2018,2019, Handbook of the 6th World Congress and School on Universal Logic, Vichy France, 2018
6. L. Blum, M.Shub, S. Smale, ?On a Theory of Computation and Complexity over the real numbers: NP-Comleness, Recursive Functions and Universal Machines, Bull.Amer.Mth.Soc.(N.S.) 21 (1): 1-46 (July 1989).
7. , M. Van Aten, On BrouwerWadsworth Philosopher?s Series, 2004 (PersianTranslation by M. Ardeshir)
8. TC+CON(TC*) deduce P is not equal to NP, F.Didehvar, Philpapers(Manuscript), 2020
9.-Theory of Fuzzy Time Computation (TC^* vs TC &TQC), hal-04330281
10. P ≠ NP, by Accepting to Make a Shift in the Theory (Time as a Fuzzy Concept), F.Didehvar, Philpapers, SSRN, 2021
11. Some Concepts and Problems in Theory of Complexity in Structures, published as ?Generalization of Some Concepts Theory in Structures?, Ph.D Thesis, 2002
12. C.Wetterich, Probabilistic Time, Foundation of Physics, 2012
13. Zeno Paradox, Unexpected Hanging Paradox (Modeling of Reality & Physical Reality, A Historical-Philosophical view), F.Didehvar, Philpapers, (Manuscript)2022 Conferences
14. When proof doesn?t show the Truth, Philosophy Day in Iran (Logic and Philosophical Logic, Tradition and Modern), 2010/11/19, Tehran, Iran.
15. A Semantic Situation without Syntax (Non-axiomatizibility of Theories), Universal Logic 2015, (5th World Congress and school, 2015/6/28, Istanbul University.
16. Is Classical Mathematics Appropriate for Theory of Computation?, Universal Logic 2018, (6th World Congress and school, 2018/6/28, Vichy University Campus.
17. Fuzzy Time, from Paradox to Paradox, The 50th Annual Iranian Mathematics Conferences, Shiraz, Iran, Shiraz University, 26-29 August, 2019, Shiraz University.
18. The impacts of Logic, Paradoxes in on side and Theory of Computation in the other side (Fuzzy Time Computation), (TC*، زمان فازی) تاثیر و تاثر منطق و پارادوکسها بر نظریه محاسبات عام 20 June 2022 (In Persian), https://ialogic.ir/index.php/2022-12-11-17-07--09/lectures/258--2022-06--15--05-07-35 The slides are in Philpapers.
19. About a Proof (TC + CON(TC ∗)Ͱ(P≠NP), The 10th Annual Conference of the Iranian Logic Association, February, 22, 2023-
Venue: Niavaran, Lecture Hall 2

10 JUL 2024
15:30 - 17:00

The problem of counting closed geodesics in Riemannian Manifolds of con- stant negative curvature has been of interest for many years. A method for counting geodesics in manifolds with arbitrary curvature is introduced by Eftekhary. Minimal surfaces in a Riemannian manifold are higher dimensional gener- alizations of closed geodesics. A natural question is how to count these types of submanifolds. We introduce a function which counts minimal tori in a Riemannian manifold (M, g) with dim M > 4. Moreover, we show that this count function is invariant under perturbations of the metric. Looking forward to seeing you organizers
Venue: Niavaran, Lecture Hall 1