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<span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 16px; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255); text-transform: none;">We would like to invite you to the next talk of the
spring in the Aalto AGC (Algebra, Geometry and Combinatorics) Seminar!</span>
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The talk is on</div>
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<b>Mon 27.4. </b>at<b> 14:15-15:00</b></div>
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in</div>
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<b>M3, Otakaari 1</b></div>
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<span style="background-color: rgb(255, 255, 255); text-transform: none;">The speaker is
</span><span style="font-family: Aptos; background-color: rgb(255, 255, 255); text-transform: none;"><b>Etna</b>
<b>Lindy </b></span></div>
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<div><span style="font-family: Aptos; font-size: 16px; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255); text-transform: none;"><b>Title</b>: Partial multiplicities of the eigenvalues of the Sylvester resultant matrix</span><span style="font-family: Aptos, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
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</span><span style="font-family: Aptos; font-size: 16px; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255); text-transform: none;"><b>Abstract</b>: Resultant matrices are polynomial matrices associated to a system of polynomials such that the coordinates
of the roots of the system are eigenvalues of the matrix.</span><span style="font-family: Aptos, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
</span><span style="font-family: Aptos; font-size: 16px; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255); text-transform: none;">In this talk, we will consider the bivariate case with two polynomials possibly sharing a multiple root.</span><span style="font-family: Aptos, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
</span><span style="font-family: Aptos; font-size: 16px; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255); text-transform: none;">It is known that the algebraic multiplicity of the eigenvalue corresponds to the multiplicity of the root.</span><span style="font-family: Aptos, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
</span><span style="font-family: Aptos; font-size: 16px; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255); text-transform: none;">In our work, we refine the connection between the multiplicities further; the partial multiplicities of the eigenvalues
can be determined from the shape of the dual vector space of the ideal. The challenging part that has not been treated in the literature earlier concerns the possible roots at infinity, to which we give a complete treatment via Möbius transformations.</span></div>
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