Question: How does mTORC1 signaling impact Notch1 expression via STAT3 activation?

Context:
Mechanistically, mTORC1 mediated IL-6-induced Stat3 activation in intestinal epithelial cells to stimulate the expression of downstream targets essential for cell proliferation and tissue regeneration. Therefore, mTORC1 signaling critically protects against inflammatory bowel disease through modulation of inflammation-induced Stat3 activity.
we demonstrated that STAT3 is directly phosphorylated by mTORC1 on Ser727 during hypoxia, promoting HIF-1α mRNA transcription
Mechanistically, mTORC1 signaling was activated by excess amino acids, which then positively regulated Notch1 expression through the activation of the signal transducer and activator of transcription 3 (STAT3).
Here we present evidence for the involvement of STAT3, a known mTORC1 regulated transcription factor, in this process
Furthermore, we demonstrated that STAT3 is directly phosphorylated by mTORC1 on Ser727 during hypoxia, promoting HIF-1α mRNA transcription. mTORC1 also regulates HIF-1α synthesis on a translational level via co-operative regulation of both initiation factor 4E-binding protein 1 (4E-BP1) and ribosomal protein S6 kinase-1 (S6K1), whereas HIF-1α degradation remains unaffected
Here we present evidence for the involvement of STAT3, a known mTORC1 regulated transcription factor, in this process. 
TSC1/TSC2 inactivation inhibits AKT through mTORC1-dependent up-regulation of STAT3-PTEN cascade.
Mechanistically, mTORC1 signaling was activated by excess amino acids, which then positively regulated Notch1 expression through the activation of the signal transducer and activator of transcription 3 (STAT3). 
Suppression of the mTORC1/STAT3/Notch1 pathway by activated AMPK prevents hepatic insulin resistance induced by excess amino acids.
Here, we review the connections between mTORC1 and gene transcription by focusing on its impact in regulating the activation of specific transcription factors including including STAT3, SREBPs, PPARγ, PPARα, HIF1α, YY1–PGC1α and TFEB. We also discuss the importance of these transcription factors in mediating the effects of mTORC1 on various cellular processes in physiological and pathological contexts.
Mechanistically, mTORC1 mediated IL-6-induced Stat3 activation in intestinal epithelial cells to stimulate the expression of downstream targets essential for cell proliferation and tissue regeneration. Therefore, mTORC1 signaling critically protects against inflammatory bowel disease through modulation of inflammation-induced Stat3 activity.
we demonstrated that STAT3 is directly phosphorylated by mTORC1 on Ser727 during hypoxia, promoting HIF-1α mRNA transcription
Mechanistically, mTORC1 signaling was activated by excess amino acids, which then positively regulated Notch1 expression through the activation of the signal transducer and activator of transcription 3 (STAT3).
Here we present evidence for the involvement of STAT3, a known mTORC1 regulated transcription factor, in this process
Furthermore, we demonstrated that STAT3 is directly phosphorylated by mTORC1 on Ser727 during hypoxia, promoting HIF-1α mRNA transcription. mTORC1 also regulates HIF-1α synthesis on a translational level via co-operative regulation of both initiation factor 4E-binding protein 1 (4E-BP1) and ribosomal protein S6 kinase-1 (S6K1), whereas HIF-1α degradation remains unaffected
Here we present evidence for the involvement of STAT3, a known mTORC1 regulated transcription factor, in this process. 
TSC1/TSC2 inactivation inhibits AKT through mTORC1-dependent up-regulation of STAT3-PTEN cascade.
Mechanistically, mTORC1 signaling was activated by excess amino acids, which then positively regulated Notch1 expression through the activation of the signal transducer and activator of transcription 3 (STAT3). 
Suppression of the mTORC1/STAT3/Notch1 pathway by activated AMPK prevents hepatic insulin resistance induced by excess amino acids.
Here, we review the connections between mTORC1 and gene transcription by focusing on its impact in regulating the activation of specific transcription factors including including STAT3, SREBPs, PPARγ, PPARα, HIF1α, YY1–PGC1α and TFEB. We also discuss the importance of these transcription factors in mediating the effects of mTORC1 on various cellular processes in physiological and pathological contexts.

Answer: mTORC1 signaling impacts Notch1 expression by positively regulating it through the activation of STAT3.