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Speaker: Utkarsh Bajaj

"Klein's icosahedral function"

Can we define a rational function on the sphere? Sure we can. Can we define a rational function on the sphere so that it is invariant under the rotational symmetries under the icosahedron? Yes - by embedding the icosahedron in the Riemann sphere (and then doing some algebra). We then show how this beautiful function reveals connections between the symmetries of the icosahedron and the E8 lattice  - the lattice that gives the most efficient packing of spheres in 8 dimensions!

MC 5501

Speaker: Filip Milidrag, University of Waterloo

"The Classification of Irreducible Discrete Reflection Groups"

In this talk we will make a correspondence between irreducible discrete reflection groups and associated connected Coxeter diagrams. Then we will use this to classify all connected Coxeter diagrams and by extension every irreducible discrete reflection group.

MC 5501

Speaker: Paul Marriott

"Statistics and Geometry: We don't talk any more."

George Bernard Shaw once said Britain and America are two counties separated by a common language. Perhaps the same can be said for Statistics and Geometry. This talk gives a high-level overview of a recent graduate course which explored the relationship between Statistics and Geometry. It looks at what the disciplines have in common but also where there are points of substantive difference. The talk will review the long history of geometric tools finding a place in statistical practice and will highlight modern developments using ideas from convex, differential and algebraic geometry and showing applications in Neuroscience.

MC 5417

Speaker: Alex Pawelko

"Symmetry Reduction and the Quest for G2 Moment Maps"

We present an overview of the classical theory of moment maps from symplectic geometry and their use within the Marsden-Weinstein-Mayer theory of symplectic reduction, with an emphasis on the Lie theoretic considerations that arise. If time permits, we will then discuss some attempts to generalize moment maps to the setting of G2 manifolds.

MC 5417

Speaker: Nicolas Chavarria

"T-minimal Theories and Dimension II"

We continue looking at Will Johnson's work on the dimension of definable sets in t-minimal theories.

MC 5403

Algebraic Geometry/Number Theory

Speaker: Cynthia Dai

"Local Heights"

In this talk, we will wrap up heights on projective space by prove Northcott's theorem for algebraic numbers. Next, we will local heights with respect to a Cartier divisor.

MC 5417

Speaker: Owen Sharpe

"An Application of Equidistribution Modulo One to Computer Graphics."

We discuss algorithms for generating pseudorandom, uniformly distributed points on the unit circle and the unit sphere. We then apply these algorithms to texture and terrain generation, using ideas from the Perlin noise scheme.

MC 5403

Research Area: Algebraic Geometry/Number Theory

Cynthia Dai

"Introduction to Naive Height"

In this seminar, we will be focusing on three results: Mordell-Weil theorem, Falting theorem, and potentially Vojta conjecture. If time permits, we will also try to cover Manin's conjecture for toric varieties. We will start slow and spend a one or two talks on naive heights on projective space, then define Weil heights for projective varieties, and study their properties. After this, we will focus on abelian varieties, and once we are familar with those objects, we introduce Neron-Tate heights, and finally prove the first main result we want to cover (actually, I think this will be all we can do this term).

For today's talk, I will review some algebraic number theory, then define Naive heights. 

MC 5417

Speaker: William Gollinger

"The Adams Spectral Sequence"

In this second lecture of the series we illustrate the spectral sequence formalism by computing some examples of the Leray-Serre spectral sequence. This tool was introduced in Serre's thesis to compute the cohomology of fibre bundles, and is much simpler to conceptualize and execute than the Adams spectral sequence. We will emphasise multiplicativity and naturality as useful tools for performing these calculations. 

MC 5417

Lucia Martin Merchan

"A Grassmannian bundle over a Spin(7) manifold"

Abstract: In this talk we study the geometry of the fiber bundle G(2,M) of oriented 2-planes on a Riemannian manifold (M,g) with a Spin(7) structure. More precisely, we construct an almost complex structure and we discuss how to compute its torsion when the holonomy of g is contained in Spin(7).

MC 5417