
PROGRAM of Lecture Courses
Tue 30 Aug 
13:00 14:30 
LUNCH 


Tue 30 Aug 
14:30 16:30 
Nakagaki, Toshiyuki "Introduction to mathematical ethology"" 
Aula Dini 
Wed 31 Aug 
Wed 31 Aug 
11:00 13:00 
Nakagaki, Toshiyuki ""Introduction to mathematical ethology"" 
Aula Dini 
Wed 31 Aug 
13:00 14:30 
LUNCH 

Wed 31 Aug 
14:30 16:30 
Yoshinaga,Masahiko
""Eulerian polynomials, lattice points counting, and arrangements." 
Aula Dini 
Thu 1 Sep 
Thu 1 Sep 
8:30 10:30 
Gaiffi, Giovanni ""Configuration spaces and representations of the symmetric group"" 
Aula Dini 
Thu 1 Sep 
10:30 11:00 
Coffee break 
Aula Dini 
Thu 1 Sep 
11:00 13:00 
Nakagaki, Toshiyuki ""Introduction to mathematical ethology""

Aula Dini 

13:00 14:30 
LUNCH 

Thu 1 Sep 
14:30 16:30 
Yoshinaga, Masahiko ""Eulerian polynomials, lattice points counting, and arrangements 
Aula Dini 

Fri 2 Sep 
Fri 2 Sep 
8:30 10:30 
Yoshinaga, Masahiko ""Eulerian polynomials, lattice points counting, and arrangements."" 
Aula Dini 
Fri 2 Sep 
10:30 11:00 
Coffee break 
Aula Dini 
Fri 2 Sep 
11:00 13:00 
Gaiffi, Giovanni ""Configuration spaces and representations of the symmetric group"" 
Aula Dini 
Fri 2 Sep 
13:00 14:30 
LUNCH 

Fri 2 Sep 
14:30 16:30 
Kubo, Hideo ""Wave equations with metric perturbation"" 
Aula Dini 

Sat 3 Sep 
Sat 3 Sep 
8:30 10:30 
Kubo, Hideo ""Wave equations with metric perturbation"" 
Aula Dini 
Sat 3 Sep 
13:00 14:30 
LUNCH 

Mon 5 Sep 

8:30 10:30 
Manca, Maria Laura " Introduction to mathematical modelling in physiology and medicine " pdffileofFirstLecture 
Aula Dini 

10:30 11:00 
Coffee break 
Aula Dini 

11:00 13:00 
Pacini, Tommaso ""Ricci flow on Riemann surfaces"

Aula Dini 

14:30 16:30 
Nakagaki, Toshiyuki ""Introduction to mathematical ethology"" 
Aula Dini 
Tue 6 Sep 

8:30 10:30 
Manca, Maria Laura " Introduction to mathematical modelling in physiology and medicine " pdffileofLecture 
Aula Dini 

10:30 11:00 
Coffee break 
Aula Dini 

11:00 13:00 
Pacini, Tommaso ""Ricci flow on Riemann surfaces" 
Aula Dini 

14:30 16:30 
Gaiffi, Giovanni ""Configuration spaces and representations of the symmetric group"" 
Aula Dini 
Wed 7 Sep 

8:30 10:30 
Manca, Maria Laura " Introduction to mathematical modelling in physiology and medicine " pdffile_of_Lecture 
Aula Dini 

10:30 11:00 
Coffee break 
Aula Dini 

11:00 13:00 
Pacini, Tommaso ""Ricci flow on Riemann surfaces" 
Aula Dini 

14:30 16:30 
Gaiffi, Giovanni ""Configuration spaces and representations of the symmetric group"" 
Aula Dini 
Thu 8 Sep 

8:30 10:30 
Manca, Maria Laura " Introduction to mathematical modelling in physiology and medicine " pdffile_of_Lecture 
Aula Dini 

10:30 11:00 
Coffee break 
Aula Dini 

11:00 13:00 
Pacini, Tommaso ""Ricci flow on Riemann surfaces" 
Aula Dini 

14:30 16:30 
Kubo, Hideo ""Wave equations with metric perturbation"" 
Aula Dini 
lecturer of the minicourse: 
title and short abstract 
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Masahiko Yoshinaga (Hokkaido University) 
Eulerian polynomials, lattice points counting, and arrangements.
Abstract: One of the most important combinatorial invariant of an arrangement is the socalled characteristic polynomial. Recently, KamiyaTakemuraTerao introduced the notion of "characteristic quasipolynomial" which is a refinement of characteristic polynomials, and has close relationships with Ehrhart quasipolynomials of rational polytopes. In this course, I would explain these materials together with Eulerian polynomials and then apply to "Riemann hypothesis for Linial arrangements" by PostnikovStanley. (Reference: arXiv:1501.04955 and references in it.) Contents: 1. Characteristic quasipolynomials of integral arrangements (due to KamiyaTakemuraTerao). 2. Ehrhart theory. (Ehrhart quasipolynomials for rational polytopes.) 3. Eulerian polynomials and root system generalizations (along the work by LamPostnikov). 4. Location of zeros of characteristic polynomials. 
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Giovanni Gaiffi (University of PISA) 
Configuration spaces and representations of the symmetric group
Orlik solomon algebras action of the symmetric group on the cohomology of the complement of the braid arrangement  compactifications of complements of arrangements (in particular De Concini Procesi models)  action of the symmetric group on the cohomology of the models of the braid arrangement some information on results for other reflection groups and open questions 
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Hideo Kubo (Hokkaido University) 
Wave equations with metric perturbation
In this lecture a systematic approach to wave equations with metric perturbation will be discussed based on the Minkowski nullframe. More precisely, our Lorentz metric is supposed to be a perturbation by the unknown function from the Minkowski metric, and we will examine which kind of assumption on the perturbation is necessary to guarantee the global existence result for small initial disturbance. Since this course is intended as an introductory one for undergraduate students, the only prerequisites will be (i) the calculus, (ii) basic functional analysis. 
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Tommaso Pacini (SNS  Pisa) 
Ricci flow on Riemann surfaces
Given a surface or a manifold, the Ricci flow is a wellknown technique for deforming its metric, trying to reach a new metric with better properties. Specifically, it is a system of Partial Differential Equations. We will examine it in the simplest case, metrics on a surface, and discuss its main properties from both the analytic and the geometric perspective. This is intended as an introductory course for undergraduates, so the only prerequisites will be (i) the geometry of curves and surfaces, and (ii) basic complex analysis.

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Toshiyuki Nakagaki (Hokkaido University) 
Introduction to mathematical ethology
Mathematical ethology is proposed as a new direction of mathematical life science: the idea is to bring equations of motion into conventional ethology (ethology is study of animal behavior). Here we primarily focus on singlecelled organisms since cell behaviors are elementary and basic in full range of organisms. In this lecture, we'd like to present some of current topics in mathematical ethology of cell and lower animal. We emphasize how standard methods of applied mathematics are used there. The aim of lecture is to show an example of how mathematical methods develop a new direction of science.
The topics we will consider are listed below.
(1) Adaptive Optimization of Foraging Network. A giant amoeba of Physarum (a single celled organism) optimizes its body shape of network form that connects spatially distributed multiple locations of food source. We consider the equations of motion for selforganizations of the optimal shape of network, and a new bioinspired method of optimal design. In this topic, some of standard methods in applied mathematics are used.
(2) Capacity of Space Memory . Ciliates like Paramecium and Tetrahymena (singlecelled swimmer by many hair called cilia emerged from surface of cell) have capacity of memorizing a shape of swimming arena. It is well known that swimming behaviors in ciliates can depend on electrical potential across the membrane, whose dynamics obeys socalled HodgkinHuxley type equations (originally proposed for excitation of squid neuron). Based on this knowledge, we will consider the mathematical model for the space memory. Some standard methods of nonlinear dynamics are introduced. This might be partially complimentary to the lecture by Prof. Maria Laura Manca.
(3) Basic mechanics of Crawling Locomotion. Crawling locomotion of lower organisms is often adaptable to a wide variety of ground conditions. Basic and general mechanics of crawling locomotion is considered. You will see the mathematical tools playing a pivotal role of understanding legless and legged crawling although they look different. 
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Maria Laura Manca
University of Pisa – Department of Clinical and Experimental Medicine 
Introduction to mathematical modelling in physiology and medicine
The 4 lessons are devoted to describe the derivation of some famous mathematical models in the fields of neuroscience and metabolism, by emphasizing how the scientists built the model. To this purpose is crucial to introduce some relevant concepts of physiology.
The topics we will consider are the following:
Lessons 1 and 2: Introduction to mathematical modelling of the biological neuron
Firstly, PhD and Master Degree students will learn that neurons are the functional units of the brain, and that they convey information using electrical and chemical signals. This is crucial for understanding the basis of the Hodgkin  Huxley mathematical model that describes how action potentials in neurons are initiated and propagated. Then the McCullochPitts model is presented, aimed to propose a different approach to describe the behaviour of neuron. Finally, we will introduce the trion model, a mathematical description of Mountcastle's model of neocortex, with particular reference to the utilization of the trion model in the explanation of the socalled “Mozart effect”
Lesson 3: Introduction to mathematical modelling of sleep
Furthermore, students will study the main mechanisms of the sleep focused to explain the most important mathematical models of sleep regulation.
Lesson 4: Introduction to mathematical modelling of insulin secretion
In the last lesson, after a description of the main actions of insulin, the Grodsky's model and the Sturis's model will be introduced.

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