Kobe Summer School (Advanced Science and technology, Undergraduate) 2014

Motohico MULASE (University of California, Davis campus)

Olivia DUMITRESCU (Leibnitz University of Hannover)

Interplay between differential equations
integrable systems and algebraic geometry

In this course, we will explain the fundamental facts about differential equations and integrable systems and their examples. We will explain the way to describe phase space in terms of algebraic geometry. Moreover, we will review recent works on its relation to quantum invariants.
(Tentative Schedule)
  1. Introduction
  2. Differential equations and integrable systems
  3. Examples
  4. A brief guide to algebraic geometry
  5. The WKB method
  6. Quantum invariants and integrable systems
  7. Further discussion I
  8. Further discussion II

Yoshiyuki TATSUMI (Professor of Earth and Planetary Sciences, Kobe University)

Drilling into the Memory of the Earth. An Introduction to International Ocean Discovery Program

The International Ocean Discovery Program (IODP) is an international marine research collaboration between 26 nations dedicated to advancing scientific understanding of the Earth using specialized ocean drilling platforms staffed by multidisciplinary research scientists. Japan is one of the leading nations of IODP and has provided a cutting-edge, riser-equipped deep sea drilling vessel, CHIKYU, which is capable of drilling up to a 7,000m deep sea floor. Internationally endorsed targets for CHIKYU are seismogeniczones that cause ultra large earthquakes such as Nankai earthquakes, intra-oceanic arcs creating continents that typify the planet Earth, and the Earth’s mantle that occupies 80% of this planet. This lecture shall introduce these projects that Japan leads.

Masahiko ARAKAWA (Professor of Earth and Planetary Sciences, Kobe University)

Earth and Planetary Sciences: Origin and Evolution of Solar System

How was our solar system formed and evolved? Our solar system has eight planets like the Earth and other various bodies such as satellites, asteroids, and comets. In this class, we learn about the origin and the characteristics of these bodies, and the recent progress of the Japanese planetary exploration of asteroids is introduced.

Yuji YAMAZAKI (Associate Professor of Physics, Kobe University)

The experiment to find the Higgs particle

In 2012, the long-awaited Higgs particle was finally found at the LHC experiment, which has let to the Nobel Prize in Physics 2013. This lecture explains about how the particle gives mass to other elementary particles and how the new particles were found experimentally.
        Lecture 1: the world of elementary particles and the Higgs particle
        Lecture 2: accelerator and experiments for finding a new particle

Wayne ROSSMAN (Professor of Mathematics, Kobe University)

How Einsten saw sphere?

In these two lectures we will use only the most basic tools from　calculus to introduce two rather remarkable theories. One is the　theory of relativity that is now so indispensable for the daily operation of modern-day life. The other is a theory that led to　Perelman‘s solution of the Poincare conjecture, which became　headline news worldwide. Our goal is to give an introduction to these two topics that is easily understood and yet still shows　their depth. We will approach this with two very down-to-earth　applications, as stated in the two titles for the lectures.
         Lecture 1: How Einstein saw spheres
         Lecture 2: The fence of least perimeter about a farm of given size

Hidehiro FUKAKI (Associate Professor of Bioligy, Kobe University)

Biology: Introduction to Plant Science

What is a plant? How do plants live? What do plants give us? This lecture provides basic knowledge on plants and discusses the importance and future of plant science.

Mitsuhiro MORITA (Associate Professor of Bioligy, Kobe University)

Evolution of the Brain

The human brain is the last frontier of modern science. Fine control of finger movement, emotion, language, and strategic planning for surviving in the wild, as well as in our society are all consequences of information processing by the brain. This talk focuses on the evolution of diverse brain functions by virtue of emerging unique neural networks.

Takuya SATO (Associate Professor of Bioligy, Kobe University)

Ecology: Exploring biodiversity in space and time

How many species inhabit planet earth? How species can co-exist, and function to maintain ecological processes, including carbon and nutrient cyclings? Students will learn basic concepts of Ecology that will be helpful in answering the above questions.

Ryousuke MATSUBARA (Associate Professor of Chemistry, Kobe University)

Chemistry: Science of Molecules

How does medicine relieve pain? How can insects lure their partner? Can we make ice-cream’s smell from petroleum? Students will learn very basic chemistry in this class and acquire the knowledge necessary to answering these questions.

Yasuhiro KOBORI (Professor of Chemistry, Kobe University)

Chemistry: photosynthesis and solar cell

How do biological molecules convert sunlight to chemical energy? How do organic solar cells generate photocurrent? Students will learn very basic quantum chemistry to understand the mechanism of photo-energy conversions.

Motohico MULASE (University of California, Davis campus)

Olivia DUMITRESCU (Leibnitz University of Hannover)

A mathematical theory of quantum curves : what they are, and what they do

The theme of the course is to present recent exciting developments　around the notion of　"quantum curves" that relates many research frontiers　of mathematics and theoretical physics. The goal is to develop a　mathematical theory of this emerging field of research.invariants. After reviewing classical theory, we will explain the theoretical background of this new field of mathematics. The quantum curves connect classical theory of differential equations and modern theory of topological invariants, such as Gromov-Witten, Seiberg-Witten, and quantum knot invariants. The course develops a universal structure of these invariants, originated by various groups of physicists, based on geometry and analysis of Riemann surfaces.
1. How do we see the moduli spaces of curves?
2. The parabola x = y2 knows the Witten-Kontsevich theory
3. Quantum invariants give the exact WKB analysis of classical ODEs
4. The simplest example of the topological recursion is Catalan numbers
5. The mathematical framework of the theory is the Hitchin fibrations
6. Geometry of ruled surfaces, log Calabi-Yau spaces, and the Hilbert scheme of points
7. From Gromov-Witten to Seiberg-Witten via a spectral curve - a glimpse of KP equations