September 16

Colloquium

4:30-5:30 pm.,

LSE 104

Arthur Baragar,

University of Nevada, Las Vegas

Constructions using a compass and twice-notched straightedge

Abstract. “It is impossible to trisect an arbitrary angle.” We (the mathematical community) have been certain of this for the past 170 years. Missing in that statement is the qualifying phrase “… using a straightedge and compass.” But if we are clumsy enough to scratch our straightedge in two places, we can in fact trisect an arbitrary angle, a result that was known to Archimedes. We are equally confident in the much more modern assertion: “There is no algorithm to solve an arbitrary quintic,” where the oft omitted qualifying phrase is “… using the extraction of roots.” In this talk, we will give an example of a quintic whose roots are not expressible using the extraction of roots, but whose real roots are constructible using a compass and twice-notched straightedge. We will also analyze the power and limitations of these tools, and present some open questions.

September 17

Number Theory Seminar

12:00-12:50 pm., PSA 206

Arthur Baragar,

University of Nevada, Las Vegas

Why I like K3 surfaces

Abstract. Click here to view.

October 20

Number Theory Seminar

12:00-12:50 pm., PSA 306

Chase Franks,

SoMSS

Determining the Lambda-module structure of Sel_E(Q_∞)_p

Abstract. Click here to view.

November 10

Number Theory Seminar

12:00-12:50 pm., PSA 306

Gary Roth,

SoMSS

Sums of squares of consecutive integers

Abstract. Click here to view.

November 17

Number Theory Seminar

2:30 - 3:20 pm.,

PSA 109

Mirela Çiperiani,

University of Texas, Austin

Tate-Shafarevich groups over anticyclotomic Z_p-extensions

Abstract. Let E be an elliptic curve over Q with supersingular reduction at p, and K an imaginary quadratic extension of Q. We analyze the structure of the Tate-Shafarevich group of E over the anticyclotomic Z_p-extension K_∞/K by viewing it as a module over Z_p[Gal(K_∞/K)].

November 18

Colloquium

4:30 - 5:30 pm.,

PSA 106

Mirela Çiperiani,

University of Texas, Austin

Genus one curves over the rationals

Abstract. We will describe what a genus one curve is and then specialize to the case of elliptic curves. After discussing a simple looking problem through which elliptic curves become objects that we want to understand, we will summarize some known results about elliptic curves. To conclude, we will go back to the general genus one curve over the rationals and see how close this object is to being an elliptic curve.

December 1

Number Theory Seminar

12:00-12:50 pm., PSA 306

Donald Adams,

SoMSS

Factorization in the ring of integers of an algebraic number field

Abstract. Click here to view.