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Title: Selected Topics in Graphs and Combinatorics.
The activity begins with a series of lectures as follows.
Speaker: Vahan Mkrtchyan, University of Yerevan (Armenia), currently on leave at the University of Verona (Italy)

  • Week 1 - Matchings and Factors in Graphs
    Perfect matchings in bipartite regular graphs.
    Tutte theorem, Berge-Tutte formula, Petersen theorem.
    r-graphs and their perfect matchings.
    Edmonds' theorem for r-graphs, Conjectures of Berge, Berge-Fulkerson and their equivalence.
    Application of Edmonds' theorem for cubic graphs.
    Related conjectures, Petersen Coloring Conjecture of Jaeger and its implications.
    The f-factor theorem, (1,2)-factors in almost regular graphs.
  • Week 2 - Edge Colorings
    The four color theorem and its reformulation in terms of edge-colorings of cubic graphs.
    The five color theorem, Fournier’s theorem, Vizing’s conjecture on planar graphs of maximum degree 6 and his result on planar graphs of maximum degree 10.
    Subsequent improvements.
    The Anderson-Goldberg-Seymour conjecture and its connections to some conjectures on r-graphs.
  • Wednesday 6 December 2017
    11.00 - 13.00 Aula M2.3 (secondo piano)
    14.00 - 16.00 Aula M2.4 (secondo piano)
  • Thursday 7 December 2017
    11.00 - 13.00 Aula M2.3 (secondo piano)
    14.00 - 15.00 Aula M2.3 (secondo piano)
  • Wednesday 13 December 2017
    11.00 - 13.00 Aula M2.3 (secondo piano)
    14.00 - 16.00 Aula M2.4 (secondo piano)
  • Thursday 14 December 2017
    11.00 - 13.00 Aula M2.3 (secondo piano)
    14.00 - 15.00 Aula M2.3 (secondo piano)
The Thursday afternoon sessions will be mainly devoted to problems and discussion

Venue: Modena, via Campi 213/B, Edificio Matematica

Next event for the activity:

Title: Some algebraic approaches to graceful labellings
Speaker: Andrea Vietri, "Sapienza" University of Rome
Abstract: Defining a graceful labelling is very easy. Finding graceful labellings requires many ad hoc techniques and is a challenging research field from decades. Finding graphs that do not admit graceful labellings leads again to some ad hoc techniques and, notably, records a basic result of algebraic nature, dating back to 1967. In this seminar, after a basic introduction we focus on that basic result and provide a generalisation by means of elementary symmetric functions. In the second half of the seminar we introduce a new algebraic tool which relates to graceful labellings, both on the existential and on the non-existential sides.

Dates: Tuesday, 9 January 2018
Venue: Modena, via Campi 213/B, Edificio Matematica, the exact time and place will be specified in a subsequent announcement.

Title: Dissipative Dynamical Systems and Applications

Teachers: Monica Conti (Politecnico di Milano), Alain Miranville (Université de Poitiers, France, and University of Xiamen, China), Giulio Schimperna (Università di Pavia)

Syllabus: The aim of the course is to draw an update picture of the research in the field of infinite dimensional dissipative dynamical systems. This geometric approach allows to analyze many models in mathematics, physics, economics, engineering and other disciplines, where the dissipation results in the confinement of the relevant long term dynamics in small portions of the phase-space. The three lecturers are expert on both the theoretical and the applied treatment of this research topic, as they all contributed in the assesment of the more suitable objects in the description of the longterm dynamics, as well as they applied their abstract results to interesting and challenging models, for instance, in material sciences and image reconstruction.

References: A reference text is A. Miranville and S. Zelik, Attractors for dissipative partial differential equations in bounded and unbounded domains, in “Handbook of Differential Equations: Evolutionary Equations, Vol. IV" (eds. C.M. Dafermos and M. Pokorny), Elsevier/North-Holland, (2008), 103-200.
Further references and/or lecture notes will be given during the course.

Dates: September 3-7, 2018
Duration: 18 hours

Title: Introduction to kinetic theory

Nei giorni 22 e 23 novembre 2016 il Prof. A. V. Bobylev - Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, terrà a Parma un mini-corso di Dottorato dal titolo “Introduction to kinetic theory”

  • Kinetic theory – what is it about? Particle dynamics and continuum mechanics.
    Distribution functions, microscopic and macroscopic models.
    Traditional and modern applications of kinetic theory.
  • From dynamics to kinetic equations. Derivation of the Boltzmann equation.
  • Boltzmann equation and its general properties. Conservation laws and H-theorem.
  • Maxwell models in kinetic theory. Fourier-Laplace transforms and general properties of Maxwell models. Spectrum of the linearized operator. Eigenfunctions and eigenvalues. Self-similar solutions, exact solutions and power-like tails.

Il corso, finanziato dallo IUSS-Ferrara 1391, si terrà presso il Dipartimento di Matematica e Informatica dell'Università di Parma, secondo il calendario riportato nella locandina allegata; la partecipazione comporta il riconoscimento di 2 CFU per attività formative disciplinari.
Tutti i dottorandi sono invitati a partecipare.

Calendario corso Prof. Alexander Bobylev