Fall 2014: Zeta Functions and Zeroes

Spring 2014 : Riemann Hypothesis & Prime Number Theorem (Chomolungma & the base camp)

Fall 2013 : Theme: Trace formulas (From Poisson to Riemann via Selberg)

Spring 2013 : Theme: Plane Algebraic Curves / Riemann Surfaces and Applications to Physics

Spring 2010 : Theme: Geometric Physics as Number Theory (see also MAT 410: Topics in Number Theory)

Fall 2014 - Fridays ...

...

Spring 2014 - Fridays 10:00-11:50 am STV 316A (<- click the link for lecture outlines)

1/24 L. Ionescu News regarding the RH (zeta function fades away! not a "diva" anymore :)

1/31 L. Ionescu Iwasawa-Tate set-up, Haran, Burnol etc.

2/7 L. I. Dynamical Zeta Functions & Reidemeister numbers

2/14 - 5/12 L.I. : see p-adic math-physics

Fall 2013 - Fridays 1:00-1:50pm in STV 313

1) 8/30 Overview: Poisson / Selberg trace formula and Riemann exact formula

2) 9/5 Poisson summation revisited (see above link)

3)

Spring 2013 - Time & room TBA

1) TBA L. Ionescu: Organizational meeting & starting "A Guide to Plane Algebraic Curves" by Keith Kendig.

2) ...

Spring 2010 - Thursdays 1pm in STV 214

1) The theme is: "Flows on Graphs".

We will learn the homological
algebra language to formulate the Min-Cut-Max-Flow Theorem, by
studying the Theory of Electric Circuits,

following A Course in Mathematics for Students of Physics, vol.2, by Bamberg and Sternberg (see some reviews here).

Contents and Introduction , Ch.12 Theory of Electrical Networks, Ch.13 The Method of Orthogonal Projections, ...

2) It is related to the famous physics problem of "What
is
the Fine Structure Constant?". following A Course in Mathematics for Students of Physics, vol.2, by Bamberg and Sternberg (see some reviews here).

Contents and Introduction , Ch.12 Theory of Electrical Networks, Ch.13 The Method of Orthogonal Projections, ...

Faculty are invited to
explore the following topics and to present them informally in
the seminar:

a) Introduction
to
Zeta functions by P. Cartier

b) Series-Parallel Networks: 1) Wolfram MathWorld; 2) by Steven Finch; 3) SP-Graphs; 4) Price of Collusion ...?

b) Series-Parallel Networks: 1) Wolfram MathWorld; 2) by Steven Finch; 3) SP-Graphs; 4) Price of Collusion ...?

2/10 L. Ionescu: "The "Biggest" Question in Physics & Flows on Graphs from a Homological Algebra viewpoint"

2/17 L. Ionescu: Introduction to Electric Circuits (or whatever else "flows") (scanned notes)

2/24 L. Ionescu: Primer of homological algebra; main example: graphs and Kirchoff's Laws (see 3rd Talk)

3/3 L.I.: Linear resistive circuits, and conceptual links (serial-parallel graphs, boolean functions, Mobius transformations etc.)

3/10 Spring break - no seminar

3/17 Conference - no seminar

3/24 LI: Review and 12.1 continued (Maxwell's methods);

3/31 R. Bernales: Visibility of 2D-lattice points and number theory (relation to EC via graphs, PoSets, lattices - same Janette ...)

4/7 LI: Hodge decomposition of electric circuits

4/14 LI: Discrete Laplacian and discrete Poisson equation

4/21 LI: Some MS-Thesis level questions of discrete mathematics: relating Hodge star operator and Maxwell's Methods for EC

4/28 LI: EC / Maxwel Methods: conclusions and interpretations; planing for next semester (last MP-seminar for Spring)

- Discrete Relative Hodge theory and Morse Theory

- Discrete Calculus (Don't be greedy: you only need enough "points", NOT the continuum!)

(Discontinued)

- Other talks: see "Recent presentations".

- For previous semesters see my ISU web page