Metabolic behaviors of proliferating cells are often explained as a rational choice to optimize cellular growth rate. In contrast, microeconomics formulates consumption behaviors as optimization problems of utilities. We pushed beyond this analogy to precisely map metabolism onto the theory of consumer choice.

We thereby revealed the correspondence between and a general mechanism for mysteries in biology and economics: the Warburg effect, a seemingly-wasteful but ubiquitous phenomenon where cells favor aerobic glycolysis over more energetically-efficient respiration, and Giffen behavior, the unexpected consumer behavior where a good is demanded more as its price rises. The correspondence implies that respiration is counterintuitively stimulated when its efficiency is decreased by drug administration.

This “microeconomics of metabolism” will serve as a macroscopic phenomenology to predict the metabolic responses against environmental operations. In particular, it offers a universal relationship between the metabolic responses against drug administrations and changes in nutrient availability.

5, 11, 17, 23, 29 are prime numbers which form an arithmetic progression of length 5. A famous theorem of Ben Green and Terence Tao in 2008 says there are arbitrarily long arithmetic progressions of prime numbers. Algebraic number theorists are also interested in more general numbers like square roots of integers. Recently, Mimura, Munemasa, Seki, Yoshino and I have established a generalization of the Green-Tao theorem in such a direction.

In the first 50 minutes of my talk, I would like to explain some background and technology behind the Green-Tao theorem. In the second half after a break, I explain the concept of number fields to formulate our generalization of their result. I will also discuss how one of the new difficulties, which I call the norm vs length conflict, is handled by a technique called Geometry of Numbers.

*Please contact Keita Mikami or Hiroyasu Miyazaki's mailing address to get access to the Zoom meeting room.

We offer a beginner’s guide to the functional-analytical techniques in quantum mechanics, and cover its application to the 1D Coulomb problem. It is shown that the wave function at the diverging point of the Coulomb potential is mathematically described by three-parameter family of generalized connection conditions. A scheme is devised to physically implement the generalized conditions, which provides the way to experimentally realize non-Rydberg spectra in 1D Hydrogen atom.

Schedule:
Part 1, Self-adjoint extension of Hilbert space operator
Part 2, 1D Coulomb problem