Despite the lockdown due to the emergency situation, the members of the math department are continuing their daily remote research activities in the best possible way. Web conferencing technologies have made it possible to continue collaborations, both within the department and with external collaborators.
Webinars
All around the world, the scientific community is organising webinars (web seminars) in order to continue to share the latest research and discuss further directions.
The webpage "mathseminars" collects a list of webinars available online, with all the details to participate and with the possibility of sorting them by topic.
Seminars organised by the Department
A list of the webinars organised by the Department. If you wish to participate, contact the responsible for the event.
Future events
Click on the events calendar
Past events
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March 27th 2020 - F. Bagagiolo and L. Marzufero (University of Trento): An Optimal Visiting Mean Field Game Problem
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April 9th 2020 - G. Giordano (University of Trento): A new epidemiological model to understand and predict the COVID-19 outbreak: the Italian case
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April 23rd 2020 - J. Iovino (University of Texas, and visiting professor at Trento), Maths Bites Trento cycle of seminars: Tao's concept of metastability as a medium connecting diverse areas of mathematics
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April 30th 2020 - G. Rinaldo and F. Romeo (University of Trento): The Hilbert series and the rook polynomial of simple thin polyominoes
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May 7th 2020 - M. Capolli (University of Trento), Doc in Progress cycle of seminars: A strange space with wormholes
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May 14th 2020 - M. Coghi (TU Berlin): McKean-Vlasov equations with common noise
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May 21st 2020 - Carina Geldhauser (University of Sheffield): Travelling waves in the stochastic Nagumo equation
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May 29th 2020 - Sara Galasso (University of Padova): Normal modes: a jump from linear to nonlinear
- June 4th 2020 - Carlo Orrieri (University of Trento), Maths Bites Trento cycle of seminars: Topics on PDEs: a probability point of view
- June 19th - Giornata di studio online: Modellistica e Covid-19
- June 19th - Nico Stollenwerk (Universidade de Lisboa, Portugal): Time scale separation: comparison of singular perturbation and center manifold analysis under scaling
- June 23rd - Nico Stollenwerk (Universidade de Lisboa, Portugal): Population biology of severe/hospitalized and mild/asymptomatic infections with SHAR-type models, case studies from dengue fever to COVID-19" with SHAR-type models, case studies from dengue fever to COVID-19
- September 30th - Nova Initia - Lectio Brevis - Benvenuto ai colleghi di Dipartimento
- October 14th - Fabio Acerbi (CNRS Parigi): Perché le matematiche bizantine sono più interessanti di quelle greche antiche
- October 15th - Valter Moretti (University of Trento): Il premio nobel per la fisica 2020 (anche) ad un teorema di matematica
- October 20th - Soumya Batthacharya (Institute of Analysis and Number Theory, Graz, Austria): Elementary divisors or the order matrix and irreducibility of holomorphic eta quotients
- October 27th - Niccolò Guicciardini (Università di Milano) Sull'interpretazione storica dei testi matematici
- October 28th - Frédéric A. Holweck (Belfort-Montbéliard): The geometry of symmetric qubit states
Research activities under pandemic emergency
Latest research produced by the Department.
Present Research activity of the group Mathematical Physics and Analytical and Geometrical Methods in Physics
Current research on:
- The construction of the Poisson algebra for functional observables of classical field theory for wave maps.
- An approach to singular potentials of delta function's kind for a single particle in non relativistic quantum mechanics in one dimension via the Resolvent Algebra approach of
- Buchholz and Grundling.
- Strict quantization map
- Theoretical aspects of quantum random numbers generators
- Path integral in Riemannian manifolds
- Spinor quantum field theory in globally hyperbolic spacetimes
- The geometric setting of variational calculus in the presence of non-holonomic
- constraints is reviewed and partially enhanced
- Generalisation of Noether theorem
- Oscillating elastic cable loaded with a mass point in the center of the span.
Latest research products and other research activities:
- Participation to the project QRANGE (Quantum Random Number Generators: cheaper, faster and more secure) H2020-FETFLAG-2018-2020
- a patent (brevetto) code 102020000005521 "Photon production device with entangled single-photon state".
Present Research activity of the group Stochastic Processes
Current research on:
- Subcritical Swift-Hohenberg equations
- Stochastic dyadic models for turbulence
- Generalized Gaussian mixtures
- Stochastic SIS models on graphs
- On evolution equations with random switching stochastic Allen-Cahn equations on graphs.
- Feynman path integrals on Riemannian manifolds
- Stochastic model of a random number generator based on silicon devices;
- Theoretical description of Quantum random number generators.
- LDPs for Kac-like walks control of interacting particle systems
Latest research products and other research activities:
- International collaborations: Augsburg (Germany), Cork (Ireland), Hagen (Germany)
- Participation to the project QRANGE (Quantum Random Number Generators: cheaper, faster and more secure) H2020-FETFLAG-2018-2020
- a patent (brevetto) code 102020000005521 "Photon production device with entangled single-photon state".
Present Research activity of the group Numerical Approximation of Partial Differential Equations
Current research on:
- Numerical methods for hyperbolic PDEs: transport of passive scalars and treatment of variable and discontinuous properties
- One-dimensional blood flow models vs lumped parameter models: development of a methodology for hybrid and real-time model selection
- Cardiovascular system modelling: construction of closed-loop models, incorporation of physiological flow and pressure control mechanisms (local and global), modelling of hypertension.
- Deep learning for physics-based model improvement in the context of non-invasive FFR prediction.
- Wave estimates for explicit finite volume schemes
- Estimation of eigenvalues of the curl operator.
Latest research products and other research activities:
- International collaborations with Trondheim (Norway), Sophia Antipolis (France), Concepción (Chile)
- Participation as speakers to international webinars.
- Preparation of scientific proposals (ERC)
Present Research activity of the group Lie Algebras, Groups, Cryptography and Codes
Current research on:
- Tensor Network, Schur Decomposition, Identifiability of rank 3 tensors, independence of cactus schemes
- Thin Lie algebras
- Regular subgroups of holomorphs, Hopf Galois structures, skew braces
- Hilbert series and primality of polyomino ideals
- Algorithms for decomposing a representation of a real semisimple Lie algebra
- Algebraic-geometric, extremal and minimal codes
- Average and worst-case complexity theory
- Finite Fields, Boolean functions and nonlinearity
- Elliptic curves and protocols based on discrete logarithms
- Polyomino ideals and Gröbner bases
- First degree prime ideals in the General Number Field Sieve
- Blockchain technologies, programming languages and security proofs
Latest research products and other research activities:
- Organisation of the series of online lectures GOThIC – Ischia Online Group Theory Conference, with 70 participants across thirteen time zones.
- International collaboration: Dubai (UAE), Lahore (India), Mumbai (India), Tel Aviv (Israel), Prague (Czech Republic), Auckland (New Zealand)
Present Research activity of the group Calculus of Variations and Geometric Measure Theory
Current research on:
- Free discontinuity variational problems with applications to materials science.
- Structure theorems for potential domains and generalizations in the context of linear partial differential operators, under assumptions of non-integrability.
- Quasilinear elliptic operators on discrete graphs in cluster analysis
- Free Boundary Monotonicity for perimeter almost-minimizers in nonsmooth convex bodies, and applications.
- Analysis of non-differentiable and quantized neural networks
- Asymptotic Wulff shapes and quantitative stability for FCC and HCP lattices
- Gamma-convergence for functional depending on vector fields
- Variational approximation for sub-Riemannian Finsler metrics.
- The Bernstein problem in the sub-Riemannian Heisenberg group
- Sobolev regularity for flows of weakly differentiable vector fields
Latest research products and other research activities:
- International collaborations: Erlangen (Germany), Cambridge (UK), Granada (Spain), Zurich (Switzerland), Munchen (Germany), Munster (Germany).
Present Research activity of the group Mathematical Logic and Theoretical Computer Science
Current research on:
- Model-theoretic investigation of logics with values in suitable Riesz spaces has been initiated, with potential applications in economics and in social sciences.
- Blockchain-related systems, the design of languages for smart contracts, and related verification techniques.
- Suitable higher inductive types within Homotopy Type Theory.
Present research activity of the group Dynamical Systems and Control Theory
Current research on:
- Consequence of Gale-Nikaido theorem
- Mean field control of flow on networks
- Mean field games with several targets
- Controllability of systems with hysteresis
Present research activity of the group Analytic and Algebraic Geometry
Current research on:
- Strength for line bundles
- Hilbert function of intersections of a hypersurface with general reducible curves
- Strength of homogeneous polynomials
- Independence of cactus schemes
- Residual resultants on toric surfaces
- Torus actions on complex projective varieties
- Rational homogeneous varieties and their characterizations in terms of positivity properties
- Construction of complex manifolds with special properties through Galois covers (rigid manifolds, Shimura subvarieties of the moduli space of curves, K3 burgers, surfaces of general type with few holomorphic differential forms,...)
- Collaborations: Bayreuth (Germany), Hannover (Germany), Strasbourg (France), Warwick (UK)
Some preprints and recent works by the Department's members
- "The impact of white noise on a supercritical bifurcation" [math.PR] [math.AP]
- “A phase-field approach to quasi-static evolution for a cohesive fracture model” [math.AP]
- “Minimality of polytopes in a nonlocal anisotropic isoperimetric problem” [math.AP]
- "Bell inequality violation by entangled single photon states generated from a laser, a LED or a Halogen lamp" [quant-ph]
- "Bulk-boundary asymptotic equivalence of two strict deformation quantizations" [quant-ph]
- "Strict deformation quantization of the state-space of $M_K(C)$ with applications to Curie-Weiss model" [math-ph]
- "On the strength of general polynomials" [math.AG]
- "The strength for line bundles" [math.AG]
- "On the Hilbert function of intersections of a hypersurface with general reducible curve" [math.AG]
- "Hysteresis and controllability of affine driftless systems: some case studies" [math.DS]
- "High rank torus actions on contact manifolds" [math. AG]
- Renegotiation and recursion in Bitcoin contracts [cs.CR]
- Coercion-Resistant Blockchain-Based E-Voting Protocol
- Primality of polyomino ideals by quadratic Gröbner basis [math.AC]
- On the weight distribution of some minimal codes [math.CO]
- A formula on the weight distribution of linear codes with applications to AMDS codes [math.CO]
- Hilbert Series of simple thin polyominoes [math.AC]
- Origin-to-destination network flow with path preferences and velocity controls: a mean field game-like approach [math-OC]
- Predicting the hotspots of age-adjusted mortality rates of lower respiratory infection across the continental United States: Integration of GIS, spatial statistics and machine learning algorithms