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

March 27th 2020  F. Bagagiolo and L. Marzufero (University of Trento): An Optimal Visiting Mean Field Game Problem

April 9th 2020  G. Giordano (University of Trento): A new epidemiological model to understand and predict the COVID19 outbreak: the Italian case

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

April 30th 2020  G. Rinaldo and F. Romeo (University of Trento): The Hilbert series and the rook polynomial of simple thin polyominoes

May 7th 2020  M. Capolli (University of Trento), Doc in Progress cycle of seminars: A strange space with wormholes

May 14th 2020  M. Coghi (TU Berlin): McKeanVlasov equations with common noise

May 21st 2020  Carina Geldhauser (University of Sheffield): Travelling waves in the stochastic Nagumo equation

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 Covid19
 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 SHARtype models, case studies from dengue fever to COVID19" with SHARtype models, case studies from dengue fever to COVID19
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 nonholonomic
 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) H2020FETFLAG20182020
 a patent (brevetto) code 102020000005521 "Photon production device with entangled singlephoton state".
Present Research activity of the group Stochastic Processes
Current research on:
 Subcritical SwiftHohenberg equations
 Stochastic dyadic models for turbulence
 Generalized Gaussian mixtures
 Stochastic SIS models on graphs
 On evolution equations with random switching stochastic AllenCahn 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 Kaclike 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) H2020FETFLAG20182020
 a patent (brevetto) code 102020000005521 "Photon production device with entangled singlephoton 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
 Onedimensional blood flow models vs lumped parameter models: development of a methodology for hybrid and realtime model selection
 Cardiovascular system modelling: construction of closedloop models, incorporation of physiological flow and pressure control mechanisms (local and global), modelling of hypertension.
 Deep learning for physicsbased model improvement in the context of noninvasive 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
 Algebraicgeometric, extremal and minimal codes
 Average and worstcase 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 nonintegrability.
 Quasilinear elliptic operators on discrete graphs in cluster analysis
 Free Boundary Monotonicity for perimeter almostminimizers in nonsmooth convex bodies, and applications.
 Analysis of nondifferentiable and quantized neural networks
 Asymptotic Wulff shapes and quantitative stability for FCC and HCP lattices
 Gammaconvergence for functional depending on vector fields
 Variational approximation for subRiemannian Finsler metrics.
 The Bernstein problem in the subRiemannian 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:
 Modeltheoretic investigation of logics with values in suitable Riesz spaces has been initiated, with potential applications in economics and in social sciences.
 Blockchainrelated 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 GaleNikaido 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 phasefield approach to quasistatic 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" [quantph]
 "Bulkboundary asymptotic equivalence of two strict deformation quantizations" [quantph]
 "Strict deformation quantization of the statespace of $M_K(C)$ with applications to CurieWeiss model" [mathph]
 "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]
 CoercionResistant BlockchainBased EVoting 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]
 Origintodestination network flow with path preferences and velocity controls: a mean field gamelike approach [mathOC]