# Undergrad Colloquium Spring 2016

McHenry Building - Room 4130

For further information please contact Richard Gottesman or call the Mathematics Department at 459-2969

**Monday April 4, 2016****No Colloquim**

**Monday April 11, 2016****No Colloquium**

**Monday April 18, 2016****No Colloquium**

**Monday April 25, 2016****No Colloqium.**

**Monday May 2, 2016****Note time change to 4pm for this talk.****Frank Bauerle, University of California, Santa Cruz**

Following Douglas Hofstadter's work in "Gōdel, Escher, Bach", we will introduce and discuss the informal formal M-I-U system. While very simple in its design, this system is surprisingly deep and fun to explore. The reason it is also useful is because it allows us to discuss properties of formal systems in general, including those that were used by Gōdel in his famous incompleteness theorems. There is no prerequisite knowledge in logic required.**Can you do MU?**

**Monday May 9, 2016**

**Monday May 16, 2016****Richard Montgomery, UCSC****Quantum Mechanics and Projective Geometry**The mathematics underlying quantum mechanics is linear algebra, specifically, linear algebra over the complex numbers with a Hermitian form center stage. We set up the standard dictionary, as set up by Dirac, between that linear algebra and quantum mechanics. As such, we are really working in complex projective space. The simplest such projective space is that for a ``two-level system'' and is `isomorphic' to the usual two-sphere. So we can ( try) to draw pictures of quantum phenomenon. We will talk a bit about Berry's phase, a quantum discovery from the 80s that has to do with parallel transport over projective space.

**Monday May 23, 2016****Abram Rodgers, UCSC***Scientific Computing, Mathematics, and Applications to Linear Algebra*Many people do not necessarily think of it too much, but programming and math go hand in hand. This talk will be on how algorithms are implemented and designed. There will also be a specific look a several implementations of linear algebra tools written by Abram Rodgers (the speaker) in C. Specific topics include some applications of linear algebra, such as simple circuits and differential equations. I will also go through the particulars of how some of the linear algebra tools were written. There will be no coding experience required, only the discussion of how one thinks of algorithms and how they are designed in a mathematical context. So do not be concerned with being unable to follow, any math/programming level should be welcome.

**Monday May 30, 2016**

***NO COLLOQUIUM* **

***HOLIDAY***