Numerical algebraic geometry uses numerical algorithms to study algebraic varieties, which are sets defined by polynomial equations.
It is becoming a core tool in applications of algebraic geometry outside of mathematics. Its fundamental concept is a witness set which gives a representation of a variety that may be manipulated on a computer. The trace test is used to verify that a witness set is complete and provide stopping criteria for algorithms. In this talk we discuss witness sets and how the trace test is used in applications. If time permits we show how a dimension reduction leads to a practical trace test for algebraic varieties in product spaces, which is the natural setting for solutions of parameterized polynomial systems. A background in algebraic geometry will not be assumed.
Joint work with Anton Leykin and Frank Sottile: https://arxiv.org/pdf/1608.00540.pdf
It is becoming a core tool in applications of algebraic geometry outside of mathematics. Its fundamental concept is a witness set which gives a representation of a variety that may be manipulated on a computer. The trace test is used to verify that a witness set is complete and provide stopping criteria for algorithms. In this talk we discuss witness sets and how the trace test is used in applications. If time permits we show how a dimension reduction leads to a practical trace test for algebraic varieties in product spaces, which is the natural setting for solutions of parameterized polynomial systems. A background in algebraic geometry will not be assumed.
Joint work with Anton Leykin and Frank Sottile: https://arxiv.org/pdf/1608.00540.pdf
Video:
https://vimeo.com/237453162
October 4 @ 12:30
12:30 pm (1h)
Discovery Building, Orchard View Room
Jose Israel Rodriquez