After introducing some open questions in the context of compact Hyperkähler manifolds, I will discuss them for some examples of HK manifolds that can be constructed from cubic fourfolds. In this case various answers can be obtained using projective algebraic geometry of cubic fourfolds. The talk is based on old and new results, as well as some work in progress with different collaborators.
The concept of quantum walks on a graph has gained popularity in the
scientific literature in recent years, likely due to its intersection
between theoretical computer science, physics, and mathematics. After
providing an overview of some popular quantum walks to illustrate their
significance in these fields, we will focus on the quantum walks
commonly referred to as "coined quantum walks" in the literature. Taking
a discrete dynamical system perspective on these quantum walks, we will
then discuss some of their transport properties in various regimes, both
random and deterministic. This discussion will highlight the differences
and similarities between coined quantum walks and classical random walks.
This initiative is part of the "PhD Lectures" activity of the project
"Departments of Excellence 2023-2027", consisting of seminars open to
Ph.D. students, followed by meetings with the speaker to discuss and go
into detail on the topics presented at the talk.
Neurodegenerative diseases such as Alzheimer’s or Parkinson’s are devastating conditions with poorly understood mechanisms and no known cure. Yet a striking feature of these conditions is the characteristic pattern of invasion throughout the brain, leading to well-codified disease stages visible to neuropathology and associated with various cognitive deficits and pathologies. This evolution is associated with the aggregation of key toxic proteins. In this talk, I will show how we use multiscale modelling to gain insight into this process and, doing so, gain some understanding on how the brain works. In particular, by looking at protein dynamics on the neuronal network, we can unravel some of the universal features associated with dementia that are driven by both the network topology and protein kinetics. By further coupling this approach with functional models of the brain, we will show that we can explain important aspects of cognitive loss during disease development.
Contatto: paola.antonietti@polimi.it
Alain Goriely is a mathematician and scientist with a broad range of interests in mathematical methods, mechanics, sciences, and engineering. He is particularly renowned for his contributions to the field of solid mechanics, both fundamental and applied, and for developing a mathematical theory of biological growth, which he explores in detail in his monograph "The Mathematics of Mechanics in Biological Growth".
Goriely earned his PhD from the University of Brussels in 1994, where he later became a lecturer. In 1996, he joined the University of Arizona and established a research group within the highly regarded Program of Applied Mathematics. In 2010, he took up a position at the University of Oxford as the inaugural Statutory Professor of Mathematical Modelling and Fellow of St. Catherine's College. He currently serves as the Director of the Oxford Centre for Industrial and Applied Mathematics.
In addition to his academic work, Goriely is also active in scientific outreach, sharing his insights and findings on a variety of topics related to his research, including tendril perversion in plants, twining plants, umbilical cord knotting, whip cracking, the shape of seashells, and brain modelling. For his contributions to mathematics and sciences, Goriely was elected as a Fellow of the Royal Society in 2022.
In this work we study the asymptotics of the fractional Laplacian as s -> 0+ on any complete Riemannian manifold (M, g), both of finite and infinite volume. Surprisingly enough, when M is not stochastically complete this asymptotics is related to the existence of bounded harmonic functions on M. As a corollary, we can find the asymptotics of the fractional s-perimeter on (essentially) every complete manifold, generalizing both the existing results: the classical result for Rn by Dipierro-Figalli-Palatucci-Valdinoci (2012) and the recent one for the Gaussian space by Carbotti-Cito-La Manna-Pallara (2021). In doing so, from many sets E contained in M we are able to produce a bounded harmonic function associated to E, which in general can be non-constant.
Alain Goriely is a mathematician and scientist with a broad range of interests in mathematical methods, mechanics, sciences, and engineering. He is particularly renowned for his contributions to the field of solid mechanics, both fundamental and applied, and for developing a mathematical theory of biological growth, which he explores in detail in his monograph "The Mathematics of Mechanics in Biological Growth".
Goriely earned his PhD from the University of Brussels in 1994, where he later became a lecturer. In 1996, he joined the University of Arizona and established a research group within the highly regarded Program of Applied Mathematics. In 2010, he took up a position at the University of Oxford as the inaugural Statutory Professor of Mathematical Modelling and Fellow of St. Catherine's College. He currently serves as the Director of the Oxford Centre for Industrial and Applied Mathematics.
In addition to his academic work, Goriely is also active in scientific outreach, sharing his insights and findings on a variety of topics related to his research, including tendril perversion in plants, twining plants, umbilical cord knotting, whip cracking, the shape of seashells, and brain modelling. For his contributions to mathematics and sciences, Goriely was elected as a Fellow of the Royal Society in 2022.
The Hilbert scheme Hilb X of n points on a quasi-projective variety X is a geometrical object introduced by Grothendieck and it has a prominent rôle in many areas of algebraic geometry. Recently, many variants of Hilb X have been introduced. My talk will focus on the double nested Hilbert scheme of points on X defined by S. Monavari. Specifically, I will explain how, when X is a smooth irreducible curve, its geometry is influenced by the combinatorics of reverse plane partitions and exhibits several pathologies. This is a joint project with Lella, Monavari, Ricolfi, Sammartano.
Alain Goriely is a mathematician and scientist with a broad range of interests in mathematical methods, mechanics, sciences, and engineering. He is particularly renowned for his contributions to the field of solid mechanics, both fundamental and applied, and for developing a mathematical theory of biological growth, which he explores in detail in his monograph "The Mathematics of Mechanics in Biological Growth".
Goriely earned his PhD from the University of Brussels in 1994, where he later became a lecturer. In 1996, he joined the University of Arizona and established a research group within the highly regarded Program of Applied Mathematics. In 2010, he took up a position at the University of Oxford as the inaugural Statutory Professor of Mathematical Modelling and Fellow of St. Catherine's College. He currently serves as the Director of the Oxford Centre for Industrial and Applied Mathematics.
In addition to his academic work, Goriely is also active in scientific outreach, sharing his insights and findings on a variety of topics related to his research, including tendril perversion in plants, twining plants, umbilical cord knotting, whip cracking, the shape of seashells, and brain modelling. For his contributions to mathematics and sciences, Goriely was elected as a Fellow of the Royal Society in 2022.
Abstract: Popular automated market makers (AMMs) use constant function markets (CFMs) to clear the demand and supply in the pool of liquidity. A key drawback in the implementation of CFMs is that liquidity providers (LPs) are currently providing liquidity at a loss, on average. In this paper, we propose two new designs for decentralised trading venues, the arithmetic liquidity pool (ALP) and the geometric liquidity pool (GLP). In both pools, LPs choose impact functions that determine how liquidity taking orders impact the marginal exchange rate of the pool, and set the price of liquidity in the form of quotes around the marginal rate. The impact functions and the quotes determine the dynamics of the marginal rate and the price of liquidity. We show that CFMs are a subset of ALP; specifically, given a trading function of a CFM, there are impact functions and quotes in the ALP that replicate the marginal rate dynamics and the execution costs in the CFM. For the ALP and GLP, we propose an optimal liquidity provision strategy where the price of liquidity maximises the LP's expected profit and the strategy depends on the LP's (i) tolerance to inventory risk and (ii) views on the demand for liquidity. Our strategies admit closed-form solutions and are computationally efficient. We show that the price of liquidity in CFMs is suboptimal in the ALP. Also, we give conditions on the impact functions and the liquidity provision strategy to prevent arbitrages from rountrip trades. Finally, we use transaction data from Binance and Uniswap v3 to show that liquidity provision is not a loss-leading activity in the ALP.
Joint work with Cartea, Drissi, Siska, and Szpruch.
Alain Goriely is a mathematician and scientist with a broad range of interests in mathematical methods, mechanics, sciences, and engineering. He is particularly renowned for his contributions to the field of solid mechanics, both fundamental and applied, and for developing a mathematical theory of biological growth, which he explores in detail in his monograph "The Mathematics of Mechanics in Biological Growth".
Goriely earned his PhD from the University of Brussels in 1994, where he later became a lecturer. In 1996, he joined the University of Arizona and established a research group within the highly regarded Program of Applied Mathematics. In 2010, he took up a position at the University of Oxford as the inaugural Statutory Professor of Mathematical Modelling and Fellow of St. Catherine's College. He currently serves as the Director of the Oxford Centre for Industrial and Applied Mathematics.
In addition to his academic work, Goriely is also active in scientific outreach, sharing his insights and findings on a variety of topics related to his research, including tendril perversion in plants, twining plants, umbilical cord knotting, whip cracking, the shape of seashells, and brain modelling. For his contributions to mathematics and sciences, Goriely was elected as a Fellow of the Royal Society in 2022.
The two function theories of monogenic and of slice monogenic functions with values in a Clifford algebra have been extensively studied in the literature. Although these functions are very different in nature they can be related via the celebrated Fueter-Sce mapping theorem or via Radon transform. In this talk we introduce a new class of functions, that of generalized partial-slice monogenic functions, which includes both of them as special cases. For this class of functions we can prove main properties such as the identity theorem, a Representation Formula, two different types of extension theorems, the Cauchy integral formula. The talk is based on a joint work with Zhenghua Xu.
Alain Goriely is a mathematician and scientist with a broad range of interests in mathematical methods, mechanics, sciences, and engineering. He is particularly renowned for his contributions to the field of solid mechanics, both fundamental and applied, and for developing a mathematical theory of biological growth, which he explores in detail in his monograph "The Mathematics of Mechanics in Biological Growth".
Goriely earned his PhD from the University of Brussels in 1994, where he later became a lecturer. In 1996, he joined the University of Arizona and established a research group within the highly regarded Program of Applied Mathematics. In 2010, he took up a position at the University of Oxford as the inaugural Statutory Professor of Mathematical Modelling and Fellow of St. Catherine's College. He currently serves as the Director of the Oxford Centre for Industrial and Applied Mathematics.
In addition to his academic work, Goriely is also active in scientific outreach, sharing his insights and findings on a variety of topics related to his research, including tendril perversion in plants, twining plants, umbilical cord knotting, whip cracking, the shape of seashells, and brain modelling. For his contributions to mathematics and sciences, Goriely was elected as a Fellow of the Royal Society in 2022.
Geomstats is an open-source Python package for computations, and statistics on nonlinear manifolds. We provide object-oriented and extensively unit-tested implementations. Manifolds can be equipped with Riemannian metrics with associated exponential and logarithmic maps, geodesics, and parallel transport. Some manifolds can also be endowed with additional mathematical structures, such as Lie group, or fiber bundle structures. Statistics and learning algorithms provide methods for estimation, clustering, and dimensionality reduction on manifolds. All associated operations are supported in different backends, namely NumPy, Autograd, and PyTorch.
In this talk, we briefly introduce the main concepts in Riemannian geometry and discuss the package design. We show that Geomstats provides reliable building blocks to both foster research in differential geometry and statistics and democratize the use of Riemannian geometry in statistics and machine learning. The source code is freely available under the MIT license at github.com/geomstats/geomstats.
Contatti:
paola.antonietti@polimi.it
edie.miglio@polimi.it
marco.verani@polimi.it
Alain Goriely is a mathematician and scientist with a broad range of interests in mathematical methods, mechanics, sciences, and engineering. He is particularly renowned for his contributions to the field of solid mechanics, both fundamental and applied, and for developing a mathematical theory of biological growth, which he explores in detail in his monograph "The Mathematics of Mechanics in Biological Growth".
Goriely earned his PhD from the University of Brussels in 1994, where he later became a lecturer. In 1996, he joined the University of Arizona and established a research group within the highly regarded Program of Applied Mathematics. In 2010, he took up a position at the University of Oxford as the inaugural Statutory Professor of Mathematical Modelling and Fellow of St. Catherine's College. He currently serves as the Director of the Oxford Centre for Industrial and Applied Mathematics.
In addition to his academic work, Goriely is also active in scientific outreach, sharing his insights and findings on a variety of topics related to his research, including tendril perversion in plants, twining plants, umbilical cord knotting, whip cracking, the shape of seashells, and brain modelling. For his contributions to mathematics and sciences, Goriely was elected as a Fellow of the Royal Society in 2022.
La teoria dei giochi, nata verso la metà del secolo scorso, è una disciplina matematica che ambisce a studiare il comportamento degli esseri umani (e non solo) nelle situazioni di interazione, in cui sia necessario compiere delle scelte strategiche. Negli ultimi decenni diversi matematici hanno vinto il premio Nobel per l'economia grazie alle loro ricerche nell'ambito della teoria dei giochi, che si è dimostrata estremamente proficua ed efficace in svariati ambiti di applicazione: politica, medicina, informatica. Nonostante ciò, le ipotesi della teoria e alcuni dei concetti fondamentali, come quello di equilibrio di Nash, sono semplici e possono essere accessibili a tutti.
In questo seminario illustreremo cosa sia la teoria dei giochi, fornendo oltre agli elementi teorici della disciplina e alcuni esempi di applicazione anche degli spunti didattici per affrontare l'argomento con gli studenti della scuola secondaria.
Alain Goriely is a mathematician and scientist with a broad range of interests in mathematical methods, mechanics, sciences, and engineering. He is particularly renowned for his contributions to the field of solid mechanics, both fundamental and applied, and for developing a mathematical theory of biological growth, which he explores in detail in his monograph "The Mathematics of Mechanics in Biological Growth".
Goriely earned his PhD from the University of Brussels in 1994, where he later became a lecturer. In 1996, he joined the University of Arizona and established a research group within the highly regarded Program of Applied Mathematics. In 2010, he took up a position at the University of Oxford as the inaugural Statutory Professor of Mathematical Modelling and Fellow of St. Catherine's College. He currently serves as the Director of the Oxford Centre for Industrial and Applied Mathematics.
In addition to his academic work, Goriely is also active in scientific outreach, sharing his insights and findings on a variety of topics related to his research, including tendril perversion in plants, twining plants, umbilical cord knotting, whip cracking, the shape of seashells, and brain modelling. For his contributions to mathematics and sciences, Goriely was elected as a Fellow of the Royal Society in 2022.
We consider the 2D Euler equations on $\mathbb{R}^2$ in vorticity form, with unbounded initial vorticity, perturbed by a suitable non-smooth Kraichnan transport noise, with regularity index $\alpha\in (0,1)$.
We show weak existence for every $\dot{H}^{-1}$ initial vorticity. Thanks to the noise, the solutions that we construct are limits in law of a regularized stochastic Euler equation and enjoy an additional $L^2([0,T];H^{-\alpha})$ regularity.
For every $p>3/2$ and for certain regularity indices $\alpha \in (0,1/2)$ of the Kraichnan noise, we show also pathwise uniqueness for every $L^p$ initial vorticity. This result is not known without noise.
Joint work with Michele Coghi.
Alain Goriely is a mathematician and scientist with a broad range of interests in mathematical methods, mechanics, sciences, and engineering. He is particularly renowned for his contributions to the field of solid mechanics, both fundamental and applied, and for developing a mathematical theory of biological growth, which he explores in detail in his monograph "The Mathematics of Mechanics in Biological Growth".
Goriely earned his PhD from the University of Brussels in 1994, where he later became a lecturer. In 1996, he joined the University of Arizona and established a research group within the highly regarded Program of Applied Mathematics. In 2010, he took up a position at the University of Oxford as the inaugural Statutory Professor of Mathematical Modelling and Fellow of St. Catherine's College. He currently serves as the Director of the Oxford Centre for Industrial and Applied Mathematics.
In addition to his academic work, Goriely is also active in scientific outreach, sharing his insights and findings on a variety of topics related to his research, including tendril perversion in plants, twining plants, umbilical cord knotting, whip cracking, the shape of seashells, and brain modelling. For his contributions to mathematics and sciences, Goriely was elected as a Fellow of the Royal Society in 2022.
Seminari Matematici al
Politecnico di Milano
- Analisi
- Cultura Matematica
- Seminari FDS
- Geometria e Algebra
- Probabilità e Statistica Matematica
- Probabilità Quantistica