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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

1 vote

approaches to Apollonius circle problems

Two circles with different radii can also be mapped to two circles with the same radius by an inversion (or a möbius transformation in general). Then the family of tangent circles is easier to describ …
Futurologist's user avatar
5 votes
Accepted

Two limit cycles which lie on the same leaf

Possibly a very "brute force" approach could be the following. Take an non-singular algebraic curve $H(x,y)=0$ given by a polynomial $H(x,y)$ with real coefficients that has at least two ovals in the …
Futurologist's user avatar
2 votes
Accepted

Question on Weil-Petersson metric on Teichmuller space

One way to define Teichmueller space is to fix a Riemann surface $X$, with a fixed complex structure, and define the space of all Beltrami differentials $\mathcal{M}(X)$ on $X$. Notice that in this wa …
Futurologist's user avatar