Title: A window into the wide world of mathematics

Abstract:

Did you ever wonder how nature decides on the shapes for double and triple bubbles? Area minimization is the key. In order to prove what bubbles have known since the beginning of time, you need to do three things:

(1) Slice and measure nature’s bubble clusters

(2) Slice and estimate measurements for arbitrary competing shapes

(3) Rigorously compare (1) and (2).

Come learn how twenty five years of research has brought a wide variety of classical ideas together with fresh insights to prove the area minimization properties of bubble clusters.

Post-test question after this talk: Which of the following methods and theorems are used in the triple bubble proof?

(a) Area-coarea formula (math 460R)

(b) Bubble identities (new)

(c) Chain rule (math 112)

(d) Divergence theorem (math 314)

(e) Eigenvalues (math 313)

(f) Factoring polynomials (math 110)

(g) Gauss Bonnet theorem (math 465)

(h) Ham Sandwich theorem (math 541)

(i) Integration by parts (math 113)

(j) Justification methods (math 290)

(k) Knowledge about computer programming (math 411)

(l) Lagrange remainder formula (math 341)

(m) Mobius transformations (math 352)

(n) Numerical analysis (math 411)

(o) Open and closed sets (math 302)

(p) Positive definite matrices (math 313)

(q) Quadratic forms (math 313)

(r) Rates of change (math 112)

(s) Second derivative test (math 112)

(t) Trigonometry (math 111)

(u) Unification (new)

(v) Vector fields (math 314)

(w) When are we ever going to use this? (math 97)

(x) Xtreme value theorem (math 341)

(y) Yesterday’s perspectives (math 300)

(z) All of zie above